2606004197
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Finite-Time Stability and Fixed-Time Stability of Stochastic Delay System with Lévy Noise

  • Jiajie Wang 1,   
  • Guanli Xiao 1,*,   
  • Yi Guan 2

Received: 29 Apr 2026 | Revised: 04 Jun 2026 | Accepted: 09 Jun 2026 | Published: 05 Aug 2026

Abstract

This paper investigates the finite-time and fixed-time stability of stochastic delay differential equations (SDDEs) driven by Lévy noise, employing Itô’s formula and the stopping-time technique. First, a novel inequality inspired by the Bihari inequality is derived, and a sufficient condition for finite-time stability of SDDEs under Lévy noise is established. Second, by integrating the Razumikhin method with Lyapunov function theory, we establish Razumikhin-type theorems that guarantee fixed-time stability and provide an explicit upper bound for the settling time. Finally, an example is given to verify the correctness of the theoretical results.

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How to Cite
Wang, J.; Xiao, G.; Guan, Y. Finite-Time Stability and Fixed-Time Stability of Stochastic Delay System with Lévy Noise. Complex Systems Stability & Control 2026, 2 (3), 10. https://doi.org/10.53941/cssc.2026.100021.
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