Wang, Y., Liu, H., & Tan, H. An Overview of Filtering for Sampled-Data Systems under Communication Constraints. International Journal of Network Dynamics and Intelligence. 2023, 2(3), 100011. doi:

Survey/Review Study

An Overview of Filtering for Sampled-Data Systems under Communication Constraints

Ye Wang 1,2, Hong-Jian Liu 1,2, and Hai-Long Tan 1,2

1 School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000, China

2 Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China


Received: 5 May 2023

Accepted: 21 July 2023

Published: 26 September 2023


Abstract: The sampled-data systems have been extensively applied to practical engineering because the digital signal shows great advantages in data transmission, storage and exchange. As a result, the analysis and synthesis problems of sampled-data systems have attracted ever-growing research interest due mainly to their significant application potential. On the other hand, the filtering or state estimation (which intends to reconstruct real system states from noisy measurements) is viewed as one of the most fundamental research topics in the control community. Until now, a lot of research efforts have been devoted to the filtering problem of sampled-data systems. The objective of the survey is to exhibit a systematic review with respect to filtering and control methods for sampled-data systems under communication constraints. First, some effective filtering algorithms are given. Then, the recent advances are shown in the filtering and control of sampled-data systems subject to network-induced phenomena based on the sampling methods. Finally, some future research topics are given on state estimation of sampled-data systems.


sampled-data system communication constraints periodic sampling aperiodic sampling filtering

1. Introduction

In the past few decades, the networked control system has shown great application potential in many fields, including the Internet of Things, chemical production and so on [1-5]. Different from the traditional point-to-point connection, the critical components in networked control systems, such as sensors, state estimators, controllers and actuators, usually transmit signals through shared wireless communication networks. The networked control system is capable of remote operation and control, which further shows great advantages of low costs and easy installation. Therefore, the networked control system has gradually become a research hotspot in the control community [6-12]. However, due mainly to the undesired constraints in wireless communication (e.g. the data processing capacity of wireless devices and the limited network bandwidth), there would inevitably exist some network-induced phenomena, such as the packet loss [13, 14], quantization [15, 16] and data saturation [17, 18]. As such, the traditional control and filtering methods may be no longer applicable in networked control systems under communication constraints. Therefore, many efforts have been devoted to the analysis and synthesis of networked control systems with communication constraints.

In networked control systems, filtering has been regarded as one of the most fundamental issues. In the existing literature, many filtering methods have been developed with various performance indexes [19-26]. Typically, for linear systems subject to Gaussian distributed white noises, the classical Kalman filtering has been viewed as the most effective filtering method since it achieves the globally optimal state estimation in the sense of the minimum filtering error covariance [19]. When there exist nonlinearities and uncertainties in the stochastic systems, it is always difficult to acquire the accurate filtering error covariance, which renders the traditional Kalman filtering invalid. In this case, the robust recursive filtering has been chosen as an alternative method in which an upper bound is guaranteed for the filtering error covariance [24]. In the case that the dynamic system is disturbed by the energy-bounded noises, the  filtering method has been proposed such that the attenuation level of estimation errors against the exogenous noises is guaranteed to be within a prespecified disturbance attenuation level [22]. Moreover, in the case that the noises can be limited into an ellipsoid, the set-membership filtering method has been developed such that the filtering errors are also constrained in an ellipsoid [25, 26].

In practice, it is a common case that the concerned plant is described as a continuous-time system, whereas the data is transmitted in a discrete-time digital form. This gives rise to the so-called sampled-data systems [27-29]. Since the sampled-data system can describe essential characteristics of practical engineering more accurately than the continuous/discrete-time system, it has received ever-growing research attention [30, 31]. To transfer continuous-time analog signals into discrete-time digital signals, sampling is an essential technique that determines whether the discrete-time signal matches the original continuous-time signal. In traditional sampled-data systems, the sampling period has been usually assumed to be a constant for the sake of simplicity. Unfortunately, due mainly to the undesired external interference (such as the shake and clock error), it is technically difficult to adopt uniform sampling. To cater for real requirements, many other sampling models have been proposed for sampled-data systems. Those available models include, but are not limited to, the bounded deterministic but uncertain sampling model [32, 33], the stochastic sampling model [34, 35], the multi-rate sampling model [22, 36], and the event-triggering sampling model [37, 38].

It should be mentioned that, the existing filtering methods have been mainly applied to continuous/discrete-time systems, and found to be inefficient in dealing with the sampled-data system. This brings great challenges to traditional filtering methods. Nowadays, many effective methods have been proposed to transform the sampled-data systems into common continuous/discrete-time systems. Typically, the discretization method directly converts the sampled-data system into the discrete-time system by utilizing the matrix exponential technique [10]. In the input-output method, the sampling period is viewed as the time delay and the sampled-data system is further equivalently denoted by the time-delay continuous-time system [39]. For multi-rate sampled-data systems, the lifting technique is the most popular method that transforms the multi-rate sampled-data systems into single-rate systems [40]. By utilizing these heuristic methods, many significant research results have been obtained on the filtering of sampled-data systems under communication constraints.

In this paper, we aim to provide a systematic review of the existing results on filtering problems for sampled-data systems with communication constraints. The remainder of this paper is outlined as follows. In Section 2, the traditional filtering method is presented. In Section 3, research results are discussed on filtering and control of sampled-data systems. Section 4 provides the conclusion and the future research topics.

2. Filtering of Networked Control Systems

Filtering is a method that reconstructs real system states from noisy measurements. Nowadays, many efforts have been devoted to developing high-accuracy and easy-to-implemented filtering schemes. The typical research results are listed as follows.

2.1. Kalman Filtering and Its Variants

In the traditional Kalman filtering proposed in [19], the globally optimal state estimate has been obtained in the minimum mean square error variance sense. Such a filtering method is able to be online implemented because the minimum filtering error covariance is derived by recursively solving the Ricatti difference equation. In this case, the Kalman filtering has gained much research attention [41-52]. Typically, the boundedness stability has been analyzed in [51] for Kalman filtering with intermittent measurements. Moreover, the probability that the filtering error covariance is bounded has been investigated in [52] over a packet-dropping network. In [41-43], constrained Kalman filters have been designed for state-constrained systems with equality/inequality constraints. In [53], a distributed Gossip Kalman filtering method has been proposed for systems over sensor networks. In [54-56], the Kalman-consistency filtering has been proposed by combining the traditional Kalman filtering method with the consistency algorithm.

When there exist nonlinearities or uncertain parameters, the classical Kalman filtering is usually inappropriate since it is usually technically impossible to obtain accurate filtering error covariances. Thus, many variants have been developed to broaden the application scope of the Kalman filtering, such as the extended Kalman filter [57-60], unscented Kalman filter [61-64], cubature Kalman filter [23, 65-67] and the robust recursive filter (RRF) [24, 68-73]. Among them, the RRF has received particular research attention due mainly to its robustness. In the RRF, an upper bound is guaranteed on the actual filtering error covariance and further minimized by designing the filter gain properly. In [71-73], the RRF has been designed for stochastic nonlinear systems. In [24, 70], the RRF has been proposed for a class of uncertain systems where the uncertainties have been described by a class of norm-bounded uncertain matrices. In [68, 69], the RRF design problem has been considered for two-dimensional systems.

2.2. Filtering

When the considered systems are subject to deterministic but energy-bounded noises, the  filtering method has been proposed such that the prescribed attenuation level of estimation errors against the exogenous noises can be reached [74-79]. In [74, 76, 77], the event-based  filtering problem has been investigated where the existence condition of the filter has been presented by a class of linear matrix inequalities. In [80, 81], the  filters have been constructed for the sampled-data systems based on the aperiodic sampling period. In [82-84], the  filtering problem has been discussed for a class of multi-rate sampled-data systems where the lifting technique has been employed to accommodate the multi-rate sampling. In [63, 85], the distributed  filtering problem has been considered for the networked control systems with network-induced phenomena.

2.3. Set-Membership Filtering

The aforementioned Kalman filtering and the  filtering both belong to the so-called point estimation where the state estimate is derived exactly. Contrarily, the set-membership filtering is a kind of interval-based state estimation method, and only obtains a reliable geometric domain to contain the state estimate. Nowadays, many set-membership filtering methods have been proposed by utilizing various of geometric domains [25, 86-96]. Typically, in [89, 90], the set-membership filters have been constructed for discrete-time systems where the intervals have been adopted to contain the state estimate. In [87, 88, 91, 92], the set-membership filtering methods have been developed such that the state estimates have been included into a class of ellipsoids. In [86, 94, 96], a new type of set-membership filtering method, named the zonotopic set-membership filtering method, has been proposed where the zonotopes and zonotope-based operations have been embedded in the set-membership filtering algorithms.

3. Filtering and Control for Sampled-data Systems

In reality, many networked control systems (NCSs) can be typically represented as continuous models. With the development of microelectronics and digital technologies, the method (of sampling continuous analog signals and converting them into discrete digital signals) has been widely used in industrial control, network communication, voice transmission, image processing and other fields. In this case, a special kind of NCSs, called the sampled-data system, has begun to attract ever-growing research attention. In what follows, we will make a brief overview of the latest results on filtering and control problems for sampled-data systems.

3.1. Periodic Sampling

In the traditional sampling method, the sampling period is usually assumed to be a constant for the sake of simplicity. Based on the periodic sampling method, a sampler is usually used to periodically sample the measurement information that is employed as the input of the filter and controller.

Consider the following continuous-time system:

where  and  are, respectively, the state and measurement outputs,  and  stand for the disturbance noises, and  and  are known matrices with appropriate dimensions. Before being transmitted to the filter, the measurement  is periodically sampled by a sampler. Thus, the following sampled-data system is further obtained.

Define the constant sampling period by

where  is the k-th sampling time instant.

In recent years, the analysis and synthesis problems of sampled-data systems with periodic sampling have received extensive research attention [97-105]. For example, in [97], the lifting technique, which converts a continuous signal into a discrete signal sequence according to the sampling time instants, has been adopted to convert the continuous-time system into an equivalent discrete-time system. Based on the sampled discrete-time signal, an  sampled-data controller has been further designed. In [98], the exponential stability has been studied for periodically sampled-data systems in the case of control input loss. Sufficient conditions for exponential stability have been obtained. Moreover, the effects have been analyzed quantitatively from the sampling period, exponential parameters, nominal packet loss rate and actual packet loss rate on the system stability. In [99], the linear quadratic control problem of periodic systems has been transformed into a sampled-data output feedback control problem, where an optimal periodic controller has been designed when the system suffers from incomplete information or measurement delays. In [100], the sampled-data output feedback control problem has been considered for a class of nonlinear systems by discretizing the high gain continuous observer. Moreover, it has been shown that, when the sampling period is sufficiently small, the performance of the continuous state feedback controller can be realized by a sampled-data controller with a sampled-data observer. In [101], by obtaining the explicit analytical solution to the nonlinear differential equation, the considered nonlinear continuous system has been discretized by periodic sampling. The discrete controller has been designed by using such a discrete model. Then, sufficient conditions have been obtained to stabilize the sampled-data systems.

3.2. Aperiodic Sampling

In practice, it is usually difficult to achieve periodic sampling owing to the unavoidable interference, such as the vibration of machines and the jitter of the pointer. In this case, the sampling period is essentially aperiodic or even random. When the sampling period has uncertainty and randomness, it will affect the performance of the concerned dynamic system and bring essential difficulties in designing of filters and controllers. Therefore, it is of practical significance to study sampled-data systems with aperiodic sampling methods (e.g. uncertain sampling [21, 27, 28, 32, 33, 106-111], stochastic sampling [30, 34, 35, 112-117], multi-rate sampling [31, 40, 118-123] and so on).

1) Uncertain Sampling

For the uncertain but deterministic sampling method, it is usually assumed that the sampling period is a bounded unknown variable. More specifically, the unknown sampling period  satisfies the following constraints

where  are the bounds determined by the sampling error of the sampler.

Nowadays, a rich body of research results have been obtained on the sampled-data systems with uncertain sampling. For example, the synchronization and state estimation problems have been investigated in [27] for a class of singularly perturbed complex networks with uncertain sampling. By utilizing the Lyapunov functional and the Kronecker product method, sufficient conditions for the exponential synchronization have been obtained for the considered complex networks. In addition, estimator gains (that guarantee the exponential stability of the estimation error system) have been further designed by adopting the matrix inequality technique. In [106], the sampled-data control input has been transformed by employing the input-output method. By constructing a time-dependent Lyapunov functional, the stability of the system has been guaranteed when the sampling period is greater than the given upper bound. In [107], the fault estimation problem has been studied for non-uniform sampled-data systems. By utilizing the input-output method, an augmented observer has been constructed to realize continuous fault estimation based on non-uniform discrete-time sampled-data measurements, which has established the foundation for fault estimation problems of non-uniform sampled-data systems. In [32], the discretization method has been used to convert the uncertain sampling period into the uncertain system parameters. Multiple norm-bounded uncertain matrices have been further employed in [28] to better describe the uncertainty caused by the sampling period.

2) Stochastic Sampling

In many cases such as the sampling of seismic data, the sampling usually occurs with a certain probability due to the influence of noises, giving rise to random characteristics. Therefore, the sampling period should be described as a random variable following a specific probability distribution.

In [112], the optimal control problem has been studied for sampled-data systems by characterizing the sampling period as a random variable obeying the Erlang distribution. More specifically, the sampling period  is modelled as

where  stands for the nominal sampling period.  is the stochastic sampling error obeying the following probability density function:

where  is the shape parameter and  is the rate parameter.

In [113], a Bernoulli distributed random variable has been utilized to describe the sampling period. Through converting the sampling period into time delays, a robust  controller has been designed for the sampled-data system with parameter uncertainties. It has been also pointed out that, the sampling period can also be assumed to switch randomly among multiple modes. Concretely, it is assumed that the sampling period  satisfies

where  are known values, and  is a given constant.

Based on this method, a sampled-data synchronization controller has been designed to guarantee the exponential mean square stability of the dynamic network in [35]. Furthermore, in [114], a sampled-data controller with random switching sampling periods has been designed in the case of data loss and adaptive time-varying delays. In [39], the random sampling method has been used to sample the measurement output and a distributed  filter has been constructed based on the sampled measurement output. In [115], the state estimation problem has been considered for neural networks with time-varying delays. By designing a sampled-data controller with random switching modes, the globally mean-square exponential stability of the estimation error system has been guaranteed for neural networks with random sampling. It is worth mentioning that, although the stochastic sampling has been considered in the existing literature, it has been always assumed that the sampling period switches randomly between two or more modes with a certain probability, which is highly conservative. In [116], random variables following an arbitrary probability distribution have been employed to model sampling errors in order to obtain a relatively perfect mathematical model. Based on this model, a sampled-data controller has been designed to ensure the stochastic stability of sampled-data systems.

3) Multi-Rate Sampling

In practice, it is usually difficult to ensure that each sensor has the same sampling period, and this gives rise to the multi-rate sampled-data systems. The multi-rate sampled-data system is usually denoted as follows:

where  is the sampling period of the plant, and  is the sampling period of the th sensor node. Moreover, the sampling period  satisfies  where  is a positive integer.

Due mainly to its great application potential, many important results have been obtained in filtering and control of multi-rate sampled-data systems. For example, in [118], the optimal sampled-data controllers have been designed for linear time-invariant systems with different A/D and D/A conversion rates. In [124], the consistency problem has been studied for sampled-data systems with multiple A/D and D/A conversion rates, and the  optimal controller has been designed by utilizing the lifting technique. In [119], the  and  filtering problems have been studied where the output sampling rate is slower than the state updating rate. It has been shown that the multi-rate sampling will cause nonconvexity, which makes it very difficult to solve the linear matrix inequalities (LMIs). Furthermore, a reduction algorithm has been proposed to solve LMIs with nonconvex constraints caused by the multi-rate sampling. In [40], the Kalman filter has been designed for multi-rate sampled-data systems where the measured transmission rate, estimated update rate and state update rate are all different from each other. In [31], the lifting technique has been adopted to transform the multi-rate sampled continuous-time system into a discrete-time system. Moreover, the state estimation and fault detection problems have been studied for the multi-rate sampled-data system. In [120, 125, 126], the fault estimation problem has been further studied for multi-rate sampled-data systems where the multi-rate systems have been transformed into signal-rate systems. In [29, 127-130], the system identification and parameter estimation problems have been studied for continuous-time systems by using the multi-rate periodic sampling method. At the same time, the controllability and observability of the original system have been analyzed. In [22, 36, 131], the fusion state estimation problem has been studied for linear multi-rate systems over sensor networks. In [132], the state estimation problem has been studied for nonlinear multi-rate systems with packet loss. In [133], the set-membership filtering problem has been considered for multi-rate systems, and a zonotope that includes the real system states has been obtained recursively.

4) Event-Triggering Sampling

Notably, the periodic sampling, the stochastic sampling and the multi-rate sampling methods can be classified as the time-based sampling methods. Although simple to implement in practical engineering, the time-based sampling methods also transmit redundant information, which takes up a lot of communication resources, especially when communication bandwidth and energy are limited. An event-triggered mechanism based sampling method is able to reduce the energy consumption and communication burden in signal transmission.

In [134], the event-triggering sampling method has been developed and further studied to solve the event-triggered PID control problem. In the event-triggered mechanism (with an irregular execution mode), the current data will not be transmitted until the triggering conditions are met, thus eliminating redundant information and reducing transmission times to save transmission energy and communication resources. So far, much research attention has been devoted to designing different types of event-triggering mechanisms such as the static event-triggering mechanisms [37, 38, 135-137], self-triggering mechanisms [138-142], and adaptive-triggering mechanisms [143-145]. It is worth mentioning that, a kind of dynamic event-triggering mechanism has been designed in [146] by introducing an internal dynamic variable related to the system state or measurement. This mechanism can further reduce the transmission times and ensure the system performance. Due mainly to its outstanding advantages, the dynamic event-triggering mechanism has attracted extensive attention [147-150]. Specifically, the control problem has been considered in [151-153] where the event-triggering mechanism has been utilized to regulate signal transmissions. In [154-156], the filtering problem has been studied where the data communication between sensors and filters has been executed by the event-triggering mechanism. In [157-159], the fusion estimation problem has been discussed for multi-sensor systems under the event-triggering mechanism. In [26, 160, 161], the event-based set-membership filtering problem has been investigated for NCSs where the error induced by the event-triggering mechanism has been transformed into the uncertainty bounded by ellipsoids.

Up to now, we have analyzed the related research results on the control and filtering problems of sampled-data systems. In the next section, we will present some future research topics.

4. Future Work for Sampled-Data Systems

4.1. More Complex Sampled-Data Systems

Although many efforts have been devoted to the filtering problem for sampled-data systems, there are still many problems to be solved. First, the stochastic sampling model is still very conservative, which should be expanded to cater for real requirements. Then, the multi-objective filtering for sampled-data systems with stochastic sampling is still a very challenging problem. Moreover, in multi-rate systems, the lifting technique is the most common method that transforms linear multi-rate systems into single-rate systems. When there exist uncertainties and nonlinearities in the systems, this method is no longer applicable, and thus new methods need to be developed. Finally, it is always the case that different sampling methods may be adopted simultaneously in sampled-data systems. In order to describe the sampled-data systems more accurately, various sampling methods should the considered at the same time, whereas the sampled-data system with mixed sampling methods has not drawn enough attention due probably to the underlying complexity and difficulty.

4.2. More Complex Network-Induced Phenomena

Although network-induced phenomena have been considered in sampled-data systems, there still exist some challenging problems that should be considered seriously. Typically, in wireless networks, the transmission distance of the signal sources (such as the sensor) is usually limited. In this case, signals broadcasted by signal sources may not be successfully transmitted to the destination (the filter and controller). In order to assure the efficient signal transmission, the relay network has been proposed where a relay (locating between the source and the destination) has been adopted to assist signal transmissions. Due mainly to its great advantages in the long-distance wireless communication, the relay network has attracted a lot of research interest from communication communities [162-164]. Accordingly, many effective relay techniques have been proposed to cater for real engineering applications such as the half-duplex relay, the virtual full-duplex relay and the full-duplex relay. Despite the fact that relay techniques have shown their potential in improving the performance of wireless networks, they will inevitably complicate the process of signal transmissions, and even cause signal distortion. Therefore, new filtering methods should be developed for sampled-data systems to accommodate the relay networks. Undoubtedly, the development of the new method will be a critical and challenging problem.

Author Contributions:  Ye Wang: data  curation,  writing—original  draft preparation; Hongjian Liu: supervision; Hailong Tan: writing—reviewing and editing. All authors have read and agreed to the published version of the manuscript.

Funding: This work was supported in part by the National Natural Science Foundation of China under Grant 62103004, the Natural Science Foundation of Anhui Province under Grant 2108085QA13, the Science and Technology Plan of Wuhu City under Grant 2022jc24.

Data Availability Statement: Not applicable.

Conflicts of Interest:  The authors declare no conflict of interest.


  1. Hossain, S.; Rahman, M.; Sarker, T.; et al. A smart IoT based system for monitoring and controlling the sub-station equipment. Internet Things, 2019, 7: 100085.
  2. El Abbadi, R.; Jamouli, H. Fault detection of a networked control system and its application to a DC motor. Int. J. Control Autom Syst., 2023, 21, 1769–1779. doi:10.1007/s12555-022-0339-6
  3. Uhm, T.; Bae, G.; Kim, J.; et al. Multiple-network-based control system design for unmanned surveillance applications. Electronics., 2023, 12, 595. doi:10.3390/electronics12030595
  4. Zhong, W.J.; Wu, Y.Q.; Li, Y.Z. Network-based formation control of unmanned autonomous systems with directed topologies. Int. J. Veh. Des., 2023, 91, 5–20. doi:10.1504/IJVD.2023.131043
  5. Bali, A.; Singh, U.P.; Kumar, R.; et al. Hybrid neural network control of uncertain switched nonlinear systems with bounded disturbance. Int. J. Robust Nonlinear Control, 2023, 33, 2651–2681. doi:10.1002/rnc.6533
  6. Gupta, R.A.; Chow, M.Y. Networked control system: Overview and research trends. IEEE Trans. Ind. Electron., 2010, 57, 2527–2535. doi:10.1109/TIE.2009.2035462
  7. Hespanha, J.P.; Naghshtabrizi, P.; Xu, Y.G. A survey of recent results in networked control systems. Proc. IEEE, 2007, 95, 138–162. doi:10.1109/JPROC.2006.887288
  8. Muthukumar, P.; Arunagirinathan, S.; Lakshmanan, S. Nonfragile sampled-data control for uncertain networked control systems with additive time-varying delays. IEEE Trans. Cybern., 2019, 49, 1512–1523. doi:10.1109/TCYB.2018.2807587
  9. Zhang, Q.C.; Zhou, Y.Y. Recent advances in non-Gaussian stochastic systems control theory and its applications. Int. J. Netw. Dyn. Intell., 2022, 1, 111–119. doi:10.53941/ijndi0101010
  10. Shen, B.; Tan, H.L.; Wang, Z.D.; et al. Quantized/Saturated control for sampled-data systems under noisy sampling intervals: A confluent vandermonde matrix approach. IEEE Trans. Automat. Control, 2017, 62, 4753–4759. doi:10.1109/TAC.2017.2685083
  11. Yao, F.; Ding, Y.L.; Hong, S.G.; et al. A survey on evolved LoRa-based communication technologies for emerging internet of things applications. Int. J. Netw. Dyn. Intell., 2022, 1, 4–19.
  12. Wang, X.L.; Sun, Y.; Ding, D.R. Adaptive dynamic programming for networked control systems under communication constraints: A survey of trends and techniques. Int. J. Netw. Dyn. Intell., 2022, 1, 85–98.
  13. Yan, H.W.; Song, X.M. A modified EKF for vehicle state estimation with partial missing measurements. IEEE Signal Process. Lett., 2022, 29, 1594–1598. doi:10.1109/LSP.2022.3189307
  14. Hu, J.; Wang, Z.D.; Liu, G.P.; et al. Event-triggered recursive state estimation for dynamical networks under randomly switching topologies and multiple missing measurements. Automatica, 2020, 115, 108908. doi:10.1016/j.automatica.2020.108908
  15. Li, Q.; Wang, Z.D.; Hu, J.; et al. Distributed state and fault estimation over sensor networks with probabilistic quantizations: The dynamic event-triggered case. Automatica, 2021, 131, 109784. doi:10.1016/j.automatica.2021.109784
  16. Wu, H.; Wang, W.; Ye, H. Set-membership state estimation with nonlinear equality constraints and quantization. Neurocomputing, 2013, 119, 359–365. doi:10.1016/j.neucom.2013.03.022
  17. Basit, A.; Tufail, M.; Rehan, M. Event-triggered distributed state estimation under unknown parameters and sensor saturations over wireless sensor networks. IEEE Trans. Circults Syst. II Express Briefs, 2022, 69, 1772–1776. doi:10.1109/TCSII.2021.3109884
  18. Qu, B.G.; Wang, Z.D.; Shen, B.; et al. Distributed state estimation for renewable energy microgrids with sensor saturations. Automatica, 2021, 131, 109730. doi:10.1016/j.automatica.2021.109730
  19. Kalman, R.E. A new approach to linear filtering and prediction problems. J. Basic Eng., 1960, 82, 35–45. doi:10.1115/1.3662552
  20. Simon, D. Kalman filtering with state constraints: A survey of linear and nonlinear algorithms. IET Control Theory and Applications, 2010, 4, 1303–1318. doi:10.1049/iet-cta.2009.0032
  21. Li, N.; Hu, J.W.; Hu, J.M.; et al. Exponential state estimation for delayed recurrent neural networks with sampled-data. Nonlinear Dyn., 2012, 69, 555–564. doi:10.1007/s11071-011-0286-x
  22. Liang, Y.; Chen, T.W.; Pan, Q. Multi-rate stochastic H∞ filtering for networked multi-sensor fusion. Automatica, 2010, 46, 437–444. doi:10.1016/j.automatica.2009.11.019
  23. Arasaratnam, I.; Haykin, S. Cubature Kalman filters. IEEE Trans. Automat. Control, 2009, 54, 1254–1269. doi:10.1109/TAC.2009.2019800
  24. Theodor, Y.; Shaked, U. Robust discrete-time minimum-variance filtering. IEEE Trans. Signal Process., 1996, 44, 181–189. doi:10.1109/78.485915
  25. Shamma, J.S.; Tu, K.Y. Set-valued observers and optimal disturbance rejection. IEEE Trans. Automat. Control, 1999, 44, 253–264. doi:10.1109/9.746252
  26. Xie, Y.H.; Ding, S.B.; Xie, X.P.; et al. Discrete-time periodic event-triggered distributed set-membership estimation over sensor networks. IEEE Trans. Signal Inf. Process. Netw., 2021, 7, 767–776. doi:10.1109/TSIPN.2021.3130435
  27. Rakkiyappan, R.; Sivaranjani, K. Sampled-data synchronization and state estimation for nonlinear singularly perturbed complex networks with time-delays. Nonlinear Dyn., 2016, 84, 1623–1636. doi:10.1007/s11071-015-2592-1
  28. Suh, Y.S. Stability and stabilization of nonuniform sampling systems. Automatica, 2008, 44, 3222–3226. doi:10.1016/j.automatica.2008.10.002
  29. Xie, L.; Yang, H.Z.; Ding, F. Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. Math. Comput. Modell., 2011, 54, 315–324. doi:10.1016/j.mcm.2011.02.014
  30. Liu, Y.J.; Lee, S.M. Sampled-data synchronization of chaotic Lur’e systems with stochastic sampling. Circuits Syst. Signal Process., 2015, 34, 3725–3739. doi:10.1007/s00034-015-0032-6
  31. Li, W.H.; Shah, S.L.; Xiao, D.Y. Kalman filters in non-uniformly sampled multirate systems: For FDI and beyond. Automatica, 2008, 44, 199–208. doi:10.1016/j.automatica.2007.05.009
  32. Oishi, Y.; Fujioka, H. Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities. Automatica, 2010, 46, 1327–1333. doi:10.1016/j.automatica.2010.05.006
  33. Hu, J.W.; Li, N.; Liu, X.H.; et al. Sampled-data state estimation for delayed neural networks with Markovian jumping parameters. Nonlinear Dyn., 2013, 73, 275–284. doi:10.1007/s11071-013-0783-1
  34. Li, H.J. Sampled-data state estimation for complex dynamical networks with time-varying delay and stochastic sampling. Neurocomputing, 2014, 138, 78–85. doi:10.1016/j.neucom.2014.02.051
  35. Shen, B.; Wang, Z.D.; Liu, X.H. Sampled-data synchronization control of dynamical networks with stochastic sampling. IEEE Trans. Automat. Control, 2012, 57, 2644–2650. doi:10.1109/TAC.2012.2190179
  36. Zhang, W.A.; Guang, F.; Yu, L. Multi-rate distributed fusion estimation for sensor networks with packet losses. Automatica, 2012, 48, 2016–2028. doi:10.1016/j.automatica.2012.06.027
  37. Lu, Q.; Han, Q.L.; Zhang, B.T.; et al. Cooperative control of mobile sensor networks for environmental monitoring: An event-triggered finite-time control scheme. IEEE Trans. Cybern., 2017, 47, 4134–4147. doi:10.1109/TCYB.2016.2601110
  38. Yang, F.W.; Xia, N.; Han, Q.L. Event-based networked islanding detection for distributed solar PV generation systems. IEEE Trans. Ind. Inf., 2017, 13, 322–329. doi:10.1109/TII.2016.2607999
  39. Shen, B.; Wang, Z.D.; Han, X.H. A stochastic sampled-data approach to distributed H∞ filtering in sensor networks. IEEE Trans. Circuits Syst. I-Regul. Pap., 2011, 58, 2237–2246. doi:10.1109/TCSI.2011.2112594
  40. Liang, Y.; Chen, T.W.; Pan, Q. Multi-rate optimal state estimation. Int. J. Control, 2009, 82, 2059–2076. doi:10.1080/00207170902906132
  41. Andersson, L.E.; Imsland, L.; Brekke, E.F.; et al. On Kalman filtering with linear state equality constraints. Automatica, 2019, 101, 467–470. doi:10.1016/j.automatica.2018.12.010
  42. Cheng, Z.J.; Ren, H.R.; Zhang, B.; et al. Distributed Kalman filter for large-scale power systems with state inequality constraints. IEEE Trans. Ind. Electron., 2021, 68, 6238–6247. doi:10.1109/TIE.2020.2994874
  43. He, X.K.; Hu, C.; Hong, Y.G.; et al. Distributed Kalman filters with state equality constraints: Time-based and event-triggered communications. IEEE Trans. Automat. Control, 2020, 65, 28–43. doi:10.1109/TAC.2019.2906462
  44. Kermarrec, G.; Jain, A.; Schön, S. Kalman filter and correlated measurement noise: The variance inflation factor. IEEE Trans. Aerosp. Electron. Syst., 2022, 58, 766–780. doi:10.1109/TAES.2021.3103564
  45. Kong, N.J.; Payne, J.J.; Council, G.; et al. The Salted Kalman filter: Kalman filtering on hybrid dynamical systems. Automatica, 2021, 131, 109752. doi:10.1016/j.automatica.2021.109752
  46. Kong, H.; Shan, M.; Sukkarieh, S.; et al. Kalman filtering under unknown inputs and norm constraints. Automatica, 2021, 133, 109871. doi:10.1016/j.automatica.2021.109871
  47. Liu, W.; Shi, P.; Wang, S.Y. Distributed Kalman filtering through trace proximity. IEEE Trans. Automat. Control, 2022, 67, 4908–4915. doi:10.1109/TAC.2022.3169956
  48. Marco, V.R.; Kalkkuhl, J.C.; Raisch, J.; et al. Regularized adaptive Kalman filter for non-persistently excited systems. Automatica, 2022, 138, 110147. doi:10.1016/j.automatica.2021.110147
  49. Moradi, A.; Venkategowda, N.K.D.; Talebi, S.P.; et al. Privacy-preserving distributed Kalman filtering. IEEE Trans. Signal Process., 2022, 70, 3074–3089. doi:10.1109/TSP.2022.3182590
  50. Xin, D.J.; Shi, L.F.; Yu, X.K. Distributed Kalman filter with faulty/reliable sensors based on Wasserstein average consensus. IEEE Trans. Circuits Syst. II Express Briefs, 2022, 69, 2371–2375. doi:10.1109/TCSII.2022.3146418
  51. Sinopoli, B.; Schenato, L.; Franceschetti, M.; et al. Kalman filtering with intermittent observations. IEEE Trans. Automat. Control, 2004, 49, 1453–1464. doi:10.1109/TAC.2004.834121
  52. Shi, L.; Epstein, M.; Murray, R.M. Kalman filtering over a packet-dropping network: A probabilistic perspective. IEEE Trans. Automat. Control, 2010, 55, 594–604. doi:10.1109/TAC.2009.2039236
  53. Kar, S.; Moura, J.M.F. Gossip and distributed Kalman filtering: Weak consensus under weak detectability. IEEE Trans. Signal Process., 2011, 59, 1766–1784. doi:10.1109/TSP.2010.2100385
  54. Olfati-Saber, R.; Shamma, J.S. Consensus filters for sensor networks and distributed sensor fusion. In Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 12–15 December 2005; IEEE: New York, USA, 2005; pp. 6698–6703. doi:10.1109/CDC.2005.1583238
  55. Olfati-Saber, R. Distributed Kalman filtering for sensor networks. In Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 12–14 December 2007; IEEE: New York, USA, 2007; pp. 5492–5498. doi:10.1109/CDC.2007.4434303
  56. Olfati-Saber, R. Kalman-consensus filter: Optimality, stability, and performance. In Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, Shanghai, China, 15–18 December 2009; IEEE: New York, 2009; pp. 7036–7042. doi:10.1109/CDC.2009.5399678
  57. Fang, H.Z.; Haile, M.A.; Wang, Y.B. Robust extended Kalman filtering for systems with measurement outlier. IEEE Trans. Control Syst. Technol., 2022, 30, 795–802. doi:10.1109/TCST.2021.3077535
  58. Beelen, H.; Bergveld, H.J.; Donkers, M.C.F. Joint estimation of battery parameters and state of charge using an extended Kalman filter: A single-parameter tuning approach. IEEE Trans. Control Syst. Technol., 2021, 29, 1087–1101. doi:10.1109/tcst.2020.2992523
  59. Barrau, A.; Bonnabel, S. Extended Kalman filtering with nonlinear equality constraints: A geometric approach. IEEE Trans. Automat. Control, 2020, 65, 2325–2338. doi:10.1109/TAC.2019.2929112
  60. Boutayeb, M.; Rafaralahy, H.; Darouach, M. Convergence analysis of the extended Kalman filter used as an observer for nonlinear deterministic discrete-time systems. IEEE Trans. Automat. Control, 1997, 42, 581–586. doi:10.1109/9.566674
  61. Julier, S.; Uhlmann, J.; Durrant-Whyte, H.F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Automat. Control, 2000, 48, 477–482. doi:10.1109/9.847726
  62. Liu, S.; Wang, Z.D.; Chen, Y.; et al. Protocol-based unscented Kalman filtering in the presence of stochastic uncertainties. IEEE Trans. Automat. Control, 2020, 65, 1303–1309. doi:10.1109/TAC.2019.2929817
  63. Ge, X.H.; Han, Q.L. Distributed event-triggered H∞ filtering over sensor networks with communication delays. Inf. Sci., 2015, 291, 128–142. doi:10.1016/j.ins.2014.08.047
  64. Daid, A.; Busvelle, E.; Aidene, M. On the convergence of the unscented Kalman filter. Eur. J. Control, 2021, 57, 125–134. doi:10.1016/j.ejcon.2020.05.003
  65. Arasaratnam, I.; Haykin, S.; Hurd, T.R. Cubature Kalman filtering for continuous-discrete systems: Theory and simulations. IEEE Trans. Signal Process., 2010, 58, 4977–4993. doi:10.1109/TSP.2010.2056923
  66. Li, Z.; Li, S.; Liu, B.; et al. A stochastic event-triggered robust cubature Kalman filtering approach to power system dynamic state estimation with non-Gaussian measurement noises. IEEE Trans. Control Syst. Technol., 2023, 31, 889–896. doi:10.1109/TCST.2022.318446710.1109/TCST.2022.3184467
  67. Zarei, J.; Shokri, E. Convergence analysis of non-linear filtering based on cubature Kalman filter. IET Sci. Meas. Technol., 2015, 9, 294–305. doi:10.1049/iet-smt.2014.0056
  68. Liang, J.L.; Wang, F.; Wang, Z.D.; et al. Robust Kalman filtering for two-dimensional systems with multiplicative noises and measurement degradations: The finite-horizon case. Automatica, 2018, 96, 166–177. doi:10.1016/j.automatica.2018.06.044
  69. Wang, F.; Wang, Z.D.; Liang, J.L.; et al. Recursive state estimation for two-dimensional shift-varying systems with random parameter perturbation and dynamical bias. Automatica, 2020, 112, 108658. doi:10.1016/j.automatica.2019.108658
  70. Tan, H.L.; Shen, B.; Shu, H.S. Robust recursive filtering for stochastic systems with time-correlated fading channels. IEEE Trans. Syst. Man Cybern. Syst., 2022, 52, 3102–3112. doi:10.1109/TSMC.2021.3062848
  71. Hu, J.; Wang, Z.D.; Liu, S.; et al. A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements. Automatica, 2016, 64, 155–162. doi:10.1016/j.automatica.2015.11.008
  72. Shen, B.; Wang, Z.D.; Wang, D.; et al. Distributed state-saturated recursive filtering over sensor networks under Round-Robin protocol. IEEE Trans. Cybern., 2020, 50, 3605–3615. doi:10.1109/TCYB.2019.2932460
  73. Wen, C.B.; Wang, Z.D.; Liu, Q.Y.; et al. Recursive distributed filtering for a class of state-saturated systems with fading measurements and quantization effects. IEEE Trans. Syst. Man Cybern. Syst., 2018, 48, 930–941. doi:10.1109/TSMC.2016.2629464
  74. Zheng, X.Y.; Zhang, H.; Wang, Z.P.; et al. Finite-time dynamic event-triggered distributed H∞ filtering for T-S fuzzy systems. IEEE Trans. Fuzzy Syst., 2022, 30, 2476–2486. doi:10.1109/TFUZZ.2021.3086560
  75. Jin, Y.; Kwon, W.; Lee, S. Further results on sampled-data H∞ filtering for T-S fuzzy systems with asynchronous premise variables. IEEE Trans. Fuzzy Syst., 2022, 30, 1864–1874. doi:10.1109/TFUZZ.2021.3069319
  76. Zhong, M.Y.; Ding, S.X.; Han, Q.L.; et al. A Krein space-based approach to event-triggered H∞ filtering for linear discrete time-varying systems. Automatica, 2022, 135, 110001. doi:10.1016/j.automatica.2021.110001
  77. Zhang, X.M.; Han, Q.L. Event-based H∞ filtering for sampled-data systems. Automatica, 2015, 51, 55–69. doi:10.1016/j.automatica.2014.10.092
  78. Ugrinovskii, V. Distributed robust filtering with H∞ consensus of estimates. Automatica, 2011, 47, 1–13. doi:10.1016/j.automatica.2010.10.002
  79. Bar Am, N.; Fridman, E. Network-based H∞ filtering of parabolic systems. Automatica, 2014, 50, 3139–3146. doi:10.1016/j.automatica.2014.10.009
  80. Li, S.Q.; Deng, F.Q.; Xing, M.L.; et al. H∞ filtering of stochastic fuzzy systems based on hybrid modeling technique with aperiodic sampled-data. Int. J. Fuzzy Syst., 2021, 23, 2106–2117. doi:10.1007/s40815-021-01080-3
  81. Chen, G.; Chen, Y.; Zeng, H.B. Event-triggered H∞ filter design for sampled-data systems with quantization. ISA Trans., 2020, 101, 170–176. doi:10.1016/j.isatra.2020.02.007
  82. Gao, R.; Yang, G.H. Distributed multi-rate sampled-data H∞ consensus filtering for cyber-physical systems under denial-of-service attacks. Inf. Sci., 2022, 587, 607–625. doi:10.1016/J.INS.2021.12.046
  83. Shen, Y.X.; Wang, Z. D.; Shen, B.; et al. H∞ filtering for multi-rate multi-sensor systems with randomly occurring sensor saturations under the p-persistent CSMA protocol. IET Control Theory Appl., 2020, 14: 1255−1265.
  84. Feng, X.L.; Wen, C.L.; Park, J.H. Sequential fusion H∞ filtering for multi-rate multi-sensor time-varying systems–a Krein-space approach. IET Control Theory Appl., 2017, 11: 369−381.
  85. Ding, D.R.; Wang, Z. D.; Shen, B.; et al. H∞ state estimation for discrete-time complex networks with randomly occurring sensor saturations and randomly varying sensor delays. IEEE Trans. Neural Netw. Learning Syst., 2012, 23: 725−736.
  86. Alamo, T.; Bravo, J.M.; Camacho, E.F. Guaranteed state estimation by zonotopes. Automatica, 2005, 41: 1035−1043.
  87. Ding, D.R.; Wang, Z.D.; Han, Q.L. A set-membership approach to event-triggered filtering for general nonlinear systems over sensor networks. IEEE Trans. Automat. Control, 2020, 65: 1792−1799.
  88. Ge, X.H.; Han, Q.L.; Wang, Z.D. A dynamic event-triggered transmission scheme for distributed set-membership estimation over wireless sensor networks. IEEE Trans. Cybern., 2019, 49: 171−183.
  89. Efimov, D.; Raïssi, T.; Chebotarev, S.; et al. Interval state observer for nonlinear time varying systems. Automatica, 2013, 49: 200−205.
  90. Tang, W.T.; Wang, Z.H.; Wang, Y.; et al. Interval estimation methods for discrete-time linear time-invariant systems. IEEE Trans. Automat. Control, 2019, 64: 4717−4724.
  91. Calafiore, G.; El Ghaoui, L. Ellipsoidal bounds for uncertain linear equations and dynamical systems. Automatica, 2004, 40: 773−787.
  92. Chernousko, F.L. Ellipsoidal state estimation for dynamical systems. Nonlinear Anal. Theory Methods Appl., 2005, 63: 872−879.
  93. Blesa, J.; Puig, V.; Saludes, J. Robust fault detection using polytope-based set-membership consistency test. IET Control Theory Appl., 2012, 6: 1767−1777.
  94. Combastel, C. An Extended Zonotopic and Gaussian Kalman Filter (EZGKF) merging set-membership and stochastic paradigms: Toward non-linear filtering and fault detection. Ann. Rev. Control, 2016, 42: 232−243.
  95. Combastel, C. Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence. Automatica, 2015, 55: 265−273.
  96. Wang, Y.; Wang, Z.H.; Puig, V.; et al. Zonotopic set-membership state estimation for discrete-time descriptor LPV systems. IEEE Trans. Automat. Control, 2019, 64: 2092−2099.
  97. Bamieh, B.A.; Pearson, J.B. A general framework for linear periodic systems with applications to H∞ sampled-data control. IEEE Trans. Automat. Control, 1992, 37: 418−435.
  98. Zhang, W.A.; Yu, L. Stabilization of sampled-data control systems with control inputs missing. IEEE Trans. Automat. Control, 2010, 55: 447−452.
  99. Yen, N.Z.; Wu, Y.C. Optimal periodic control implemented as a generalized sampled-data hold output feedback control. IEEE Trans. Automat. Control, 1993, 38: 1560−1563.
  100. Dabroom, A.M.; Khalil, H.K. Output feedback sampled-data control of nonlinear systems using high-gain observers. IEEE Trans. Automat. Control, 2001, 46: 1712−1725.
  101. Nesic, D.; Teel, A.R. A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Trans. Automat. Control, 2004, 49: 1103−1122.
  102. Hu, L.S.; Bai, T.; Shi, P.; et al. Sampled-data control of networked linear control systems. Automatica, 2007, 43: 903−911.
  103. Katayama, H.; Ichikawa, A. H∞ control for sampled-data nonlinear systems described by Takagi-Sugeno fuzzy systems. Fuzzy Sets Syst. 2004, 148, 431–452. doi:10.1016/j.fss.2003.12.009
  104. Ortiz, D.S.; Freudenberg, J.S.; Middleton, R.H. Feedback limitations of linear sampled-data periodic digital control. Int. J. Robust Nonlinear Control, 2000, 10: 729−745.
  105. Nguang, S.K.; Shi, P. On designing filters for uncertain sampled-data nonlinear systems. Systems & Control Letters, 2000, 41: 305−316.
  106. Ding, F.; Qiu, L.; Chen, T.W. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica, 2009, 45, 324–332. doi:10.1016/j.automatica.2008.08.007
  107. Wen, C.L.; Qiu, A.B.; Jiang, B. An output delay approach to fault estimation for sampled-data systems. Sci. China: Inf. Sci., 2012, 55, 2128–2138. doi:10.1007/s11432-011-4472-8
  108. Suplin, V.; Fridman, E.; Shaked, U. Sampled-data H∞ control and filtering: Nonuniform uncertain sampling. Automatica, 2007, 43, 1072–1083. doi:10.1016/j.automatica.2006.11.024
  109. Li, N.; Zhang, Y.L.; Hu, J.W.; et al. Synchronization for general complex dynamical networks with sampled-data. Neurocomputing, 2011, 74, 805–811. doi:10.1016/j.neucom.2010.11.007
  110. Wu, Z.G.; Shi, P.; Su, H.Y. et al. Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data. IEEE Trans. Cybern., 2013, 43, 1796–1806. doi:10.1109/TSMCB.2012.2230441
  111. Yang, F.S.; Zhang, H.G.; Wang, Y.C. An enhanced input-delay approach to sampled-data stabilization of T-S fuzzy systems via mixed convex combination. Nonlinear Dyn., 2014, 75, 501–512. doi:10.1007/s11071-013-1080-8
  112. Kanchanaharuthai, A.; Wongsaisuwan, M. Stochastic H2-optimal controller design for sampled-data systems with random sampled measurement. In Proceedings of the 41st SICE Annual Conference, Osaka, Japan, 5–7 August 2002; IEEE: New York, USA, 2002; pp. 2042–2047. doi:10.1109/SICE.2002.1196647
  113. Gao, H.J.; Wu, J.L.; Shi, P. Robust sampled-data H∞ control with stochastic sampling. Automatica, 2009, 45, 1729–1736. doi:10.1016/j.automatica.2009.03.004
  114. Rakkiyappan, R.; Sakthivel, N.; Cao, J.D. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Neural Netw., 2015, 66, 46–63. doi:10.1016/j.neunet.2015.02.011
  115. Lee, T.H.; Park, J.H.; Kwon, O.M.; et al. Stochastic sampled-data control for state estimation of time-varying delayed neural networks. Neural Netw., 2013, 46, 99–108. doi:10.1016/j.neunet.2013.05.001
  116. Shen, B.; Wang, Z.D.; Huang, T.W. Stabilization for sampled-data systems under noisy sampling interval. Automatica, 2016, 63, 162–166. doi:10.1016/j.automatica.2015.10.005
  117. Rakkiyappan, R.; Sivasamy, R.; Cao, J.D. Stochastic sampled-data stabilization of neural-network-based control systems. Nonlinear Dyn., 2015, 81, 1823–1839. doi:10.1007/s11071-015-2110-5
  118. Chen, T.; Francis, B.A. H2 optimal sampled-data control. IEEE Trans. Automat. Control, 1991, 36, 387–397. doi:10.1109/9.75098
  119. Sheng, J.; Chen, T.W.; Shah, S.L. Optimal filtering for multirate systems. IEEE Trans. Circuits Syst. II Express Briefs, 2005, 52, 228–232. doi:10.1109/TCSII.2004.842009
  120. Izadi, I.; Zhao, Q.; Chen, T.W. An optimal scheme for fast rate fault detection based on multirate sampled data. J. Process Control, 2005, 15, 307–319. doi:10.1016/j.jprocont.2004.06.008
  121. Geng, H.; Liang, Y.; Yang, F.; et al. Model-reduced fault detection for multi-rate sensor fusion with unknown inputs. Inf. Fusion, 2017, 33, 1–14. doi:10.1016/j.inffus.2016.04.002
  122. Tanasa, V.; Monaco, S.; Normand-Cyrot, D. Backstepping control under multi-rate sampling. IEEE Trans. Automat. Control, 2016, 61, 1208–1222. doi:10.1109/TAC.2015.2453891
  123. Li, N.; Sun, S.L.; Ma, J. Multi-sensor distributed fusion filtering for networked systems with different delay and loss rates. Digital Signal Process., 2014, 34, 29–38. doi:10.1016/j.dsp.2014.07.016
  124. Qiu, L.; Chen, T.W. H2 optimal design of multirate sampled-data systems. IEEE Trans. Automat. Control, 1994, 39, 2506–2511. doi:10.1109/9.362836
  125. Fadali, M.S. Observer-based robust fault detection of multirate linear system using a lift reformulation. Comput. Electr. Eng., 2003, 29, 235–243. doi:10.1016/S0045-7906(01)00008-8
  126. Zhang, P.; Ding, S.X.; Wang, G.Z.; et al. Fault detection for multirate sampled-data systems with time delays. Int. J. Control, 2002, 75, 1457–1471. doi:10.1080/0020717021000031475
  127. Ding, F.; Liu, G.J.; Liu, X.P. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Automat. Control, 2010, 55, 1976–1981. doi:10.1109/TAC.2010.2050713
  128. Han, L.L.; Ding, F. Identification for multirate multi-input systems using the multi-innovation identification theory. Comput. Math. Appl., 2009, 57, 1438–1449. doi:10.1016/j.camwa.2009.01.005
  129. Liu, Y.J.; Ding, F.; Shi, Y. Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Syst. Signal Process., 2012, 31, 1985–2000. doi:10.1007/s00034-012-9421-2
  130. Xie, L.; Liu, Y.J.; Yang, H.Z.; et al. Modelling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl., 2010, 4, 784–794. doi:10.1049/iet-cta.2009.0064
  131. Zhang, W.A.; Liu, S.; Yu, Y. Fusion estimation for sensor networks with nonuniform estimation rates. IEEE Trans. Circuits Syst. I Regul. Pap., 2014, 61, 1485–1498. doi:10.1109/TCSI.2013.2285693
  132. Yan, L.P.; Xiao, B.; Xia, Y.Q.; et al. State estimation for asynchronous multirate multisensor nonlinear dynamic systems with missing measurements. Int. J. Adapt. Control Signal Process., 2012, 26, 516–529. doi:10.1002/acs.2266
  133. Orihuela, L.; Roshany-Yamchi, S.; García, R.A.; et al. Distributed set-membership observers for interconnected multi-rate systems, Automatica, 2017, 85, 221–226. doi:10.1016/j.automatica.2017.07.041
  134. Årzén, K.E. A simple event-based PID controller. In Proceedings of the 14th IFAC World Congress, Beijing, China, 5–9 July 1999; 1999; pp. 423–428.
  135. Chen, X.; Hao, F. Event-triggered average consensus control for discrete-time multi-agent systems. IET Control Theory Appl., 2012, 6, 2493–2498. doi:10.1049/iet-cta.2011.0535
  136. Miskowicz, M. Send-on-delta concept: An event-based data reporting strategy. Sensors, 2006, 6, 49–63. doi:10.3390/s6010049
  137. Shen, H.; Fu, L.; Yan, H.C.; et al. Finite-time event-triggered H∞ control for T-S fuzzy Markov jump systems. IEEE Trans. Fuzzy Syst., 2018, 26, 3122–3135. doi:10.1109/TFUZZ.2017.2788891
  138. Anta, A.; Tabuada, P. To sample or not to sample: Self-triggered control for nonlinear systems. IEEE Trans. Automat. Control, 2010, 55, 2030–2042. doi:10.1109/TAC.2010.2042980
  139. Gao, Y.L.; Yu, P.; Dimarogonas, D.V.; et al. Robust self-triggered control for time-varying and uncertain constrained systems via reachability analysis. Automatica, 2019, 107, 574–581. doi:10.1016/j.automatica.2019.06.015
  140. Wang, X.F.; Lemmon, M.D. Self-triggered feedback control systems with finite-gain L2 stability. IEEE Trans. Automat. Control, 2009, 54, 452–467. doi:10.1109/TAC.2009.2012973
  141. Xu, W.Y.; Ho, D.W.C.; Zhang, J.; et al. Event/self-triggered control for leader-following consensus over unreliable network with DoS attacks. IEEE Trans. Neural Netw. Learn. Syst., 2019, 30, 3137–3149. doi:10.1109/TNNLS.2018.2890119
  142. Yi, X.L.; Liu, K.; Dimarogonas, D.V.; et al. Dynamic event-triggered and self-triggered control for multi-agent systems. IEEE Trans. Automat. Control, 2019, 64, 3300–3307. doi:10.1109/TAC.2018.2874703
  143. Li, H.Y.; Zhang, Z.X.; Yan, H.C.; et al. Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern., 2019, 49, 4388–4397. doi:10.1109/TCYB.2018.2864776
  144. Peng, C.; Zhang, J.; Yan, H.C. Adaptive event-triggered H∞ load frequency control for network-based power systems. IEEE Trans. Ind. Electron., 2018, 65, 1685–1694. doi:10.1109/TIE.2017.2726965
  145. Zhang, H.; Wang, Z.P.; Yan, H.C.; et al. Adaptive event-triggered transmission scheme and H∞ filtering co-design over a filtering network with switching topology. IEEE Trans. Cybern., 2019, 49, 4296–4307. doi:10.1109/TCYB.2018.2862828
  146. Girard, A. Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Automat. Control, 2015, 60, 1992–1997. doi:10.1109/TAC.2014.2366855
  147. Dolk, V.S.; Borgers, D.P.; Heemels, W.P.M.H. Output-based and decentralized dynamic event-triggered control with guaranteed Lp-gain performance and zeno-freeness. IEEE Trans. Automat. Control, 2017, 62, 34–49. doi:10.1109/TAC.2016.2536707
  148. Ge, X.H.; Han, Q.L. Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans. Ind. Electron., 2017, 64, 8118–8127. doi:10.1109/TIE.2017.2701778
  149. Hu, S.L.; Yue, D.; Yin, X.X.; et al. Adaptive event-triggered control for nonlinear discrete-time systems. Int. J. Robust Nonlinear Control, 2016, 26, 4104–4125. doi:10.1002/rnc.3550
  150. Wang, Y.C.; Zheng, W.X.; Zhang, H.G. Dynamic event-based control of nonlinear stochastic systems. IEEE Trans. Automat. Control, 2017, 62, 6544–6551. doi:10.1109/TAC.2017.2707520
  151. Dimarogonas, D.V.; Frazzoli, E.; Johansson, K.H. Distributed event-triggered control for multi-agent systems. IEEE Trans. Automat. Control, 2012, 57, 1291–1297. doi:10.1109/TAC.2011.2174666
  152. Ding, D.R.; Wang, Z.D.; Wei, G.L.; et al. Event-based security control for discrete-time stochastic systems. IET Control Theory Appl., 2016, 10, 1808–1815. doi:10.1049/iet-cta.2016.0135
  153. Lunze, J.; Lehmann, D. A state-feedback approach to event-based control. Automatica, 2010, 46, 211–215. doi:10.1016/j.automatica.2009.10.035
  154. Han, D.; Mo, Y.L.; Wu, J.F.; et al. Stochastic event-triggered sensor schedule for remote state estimation. IEEE Trans. Automat. Control, 2015, 60: 2661−2675.
  155. Li, Q.; Shen, B.; Liu, Y.R.; et al. Event-triggered H∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing, 2016, 174: 912−920.
  156. Zou, L.; Wang, Z.D.; Gao, H.J.; et al. Event-triggered state estimation for complex networks with mixed time delays via sampled data information: The continuous-time case. IEEE Trans. Cybern., 2015, 45: 2804−2815.
  157. Li, L.; Niu, M.F.; Xia, Y.Q.; et al. Event-triggered distributed fusion estimation with random transmission delays. Inf. Sci., 2019, 475: 67−81.
  158. Tan, H.L.; Shen, B.; Liu, Y.R.; et al. Event-triggered multi-rate fusion estimation for uncertain system with stochastic nonlinearities and colored measurement noises. Inf. Fusion, 2017, 36: 313−320.
  159. Wang, Z.D.; Hu, J.; Ma, L.F. Event-based distributed information fusion over sensor networks. Inf. Fusion, 2018, 39: 53−55.
  160. Bai, X.Z.; Wang, Z.D.; Zou, L.; et al. Target tracking for wireless localization systems using set-membership filtering: A component-based event-triggered mechanism. Automatica, 2021, 132: 109795.
  161. Fan, S.; Yan, H.C.; Zhan, X.S.; et al. Distributed set-membership estimation for state-saturated systems with mixed time-delays via a dynamic event-triggered scheme. J. Franklin Inst., 2021, 358: 10079−10094.
  162. El-Zahr, S.; Abou-Rjeily, C. Buffer state based relay selection for half-duplex buffer-aided serial relaying systems. IEEE Trans. Commun., 2022, 70: 3668−3681.
  163. Kim, S.M.; Bengtsson, M. Virtual full-duplex buffer-aided relaying in the presence of inter-relay interference. IEEE Trans. Wireless Commun., 2016, 15: 2966−2980.
  164. Liu, G.; Yu, F.R.; Ji, H.; et al. In-band full-duplex relaying: A survey, research issues and challenges. IEEE Commun. Surv. Tutorials, 2015, 17: 500−524.