Stability of nonlinear stochastic systems with delayed impulses under self-triggered impulsive control

Bing Shang; Jin-E Zhang; Bing Shang; Jin-E Zhang

doi:10.3934/math.2025910

AIMS Mathematics

2025, Volume 10, Issue 9: 20368-20384. doi: 10.3934/math.2025910

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Research article

Stability of nonlinear stochastic systems with delayed impulses under self-triggered impulsive control

Bing Shang ,
Jin-E Zhang ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received: 17 July 2025 Revised: 25 August 2025 Accepted: 28 August 2025 Published: 05 September 2025
MSC : 93C30

This paper investigates the stability problem of nonlinear stochastic systems with delayed impulses based on a self-triggered impulsive control (STIC) strategy. By employing the Lyapunov method, an explicit self-triggering mechanism (STM) with state-dependent waiting time parameters is designed, which ensures system stability while effectively avoiding Zeno behavior. Compared with traditional event-triggered impulsive control (ETIC) methods, this strategy does not require continuous state monitoring and can determine the next triggering instant based on the currently available state information. Furthermore, the developed theoretical results are applied to the STIC problem of nonlinear stochastic systems. Finally, the effectiveness and feasibility of the proposed method are validated through two numerical examples.
- nonlinear stochastic system,
- stability,
- delayed impulses,
- self-triggered impulsive control
Citation: Bing Shang, Jin-E Zhang. Stability of nonlinear stochastic systems with delayed impulses under self-triggered impulsive control[J]. AIMS Mathematics, 2025, 10(9): 20368-20384. doi: 10.3934/math.2025910

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Abstract

This paper investigates the stability problem of nonlinear stochastic systems with delayed impulses based on a self-triggered impulsive control (STIC) strategy. By employing the Lyapunov method, an explicit self-triggering mechanism (STM) with state-dependent waiting time parameters is designed, which ensures system stability while effectively avoiding Zeno behavior. Compared with traditional event-triggered impulsive control (ETIC) methods, this strategy does not require continuous state monitoring and can determine the next triggering instant based on the currently available state information. Furthermore, the developed theoretical results are applied to the STIC problem of nonlinear stochastic systems. Finally, the effectiveness and feasibility of the proposed method are validated through two numerical examples.

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