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<p>This paper focuses on the Lyapunov-Razumikhin method for finite-time stability (FTS) in probability of impulsive stochastic delayed systems (ISDSs). To establish these properties, several Lyapunov-based Razumikhin conditions on FTS for ISDSs are derived by employing the comparison principle, which explicitly incorporate delay-dependent factors. Therefore, the conservativeness is less. Then, the theoretical results are utilized to address the problem of finite-time consensus in a class of stochastic delayed multi-agent systems by a designed hybrid controller, which includes an impulsive controller and a finite-time controller. It is noted that the finite-time controller contains no sign function that can avoid the chattering phenomenon caused by control signals. At last, a numerical example is presented to demonstrate the validity of the results obtained.</p>

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Razumikhin-type Theorem on Finite-time Stability of Impulsive Stochastic Delayed Systems and Applications to Multi-agent Systems

  • 期刊论文

  • 发表日期：

    2025年4月12日

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  • Tao Chen,
  • Shiguo Peng,
  • Zhiwen Fu

摘要

This paper focuses on the Lyapunov-Razumikhin method for finite-time stability (FTS) in probability of impulsive stochastic delayed systems (ISDSs). To establish these properties, several Lyapunov-based Razumikhin conditions on FTS for ISDSs are derived by employing the comparison principle, which explicitly incorporate delay-dependent factors. Therefore, the conservativeness is less. Then, the theoretical results are utilized to address the problem of finite-time consensus in a class of stochastic delayed multi-agent systems by a designed hybrid controller, which includes an impulsive controller and a finite-time controller. It is noted that the finite-time controller contains no sign function that can avoid the chattering phenomenon caused by control signals. At last, a numerical example is presented to demonstrate the validity of the results obtained.