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Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control

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Listed:
  • Xia, Mingli
  • Liu, Linna
  • Fang, Jianyin
  • Qu, Boyang

Abstract

This paper investigates the stabilization of stochastic differential systems with exogenous disturbance inputs by employing an event-triggered impulsive control (ETIC) strategy. Firstly, an event-triggered mechanism (ETM) is put forward consisting of an exponentially decreasing function and exogenous disturbance terms. Moreover, through the incorporation of a state-dependent waiting time, Zeno phenomenon in the system can be completely avoided. Then sufficient conditions for exponentially weighted input-to-state stability (eλt-ISS) of systems can be obtained based on Lyapunov function method and Itô’s formula under some reasonable criteria. Specifically, theoretical results establish a relationship between waiting time and trigger parameters. By altering the value of trigger parameters, it becomes feasible to adjust event-triggered time and control the frequency of activated impulses accordingly. In the end, two numerical examples are given to demonstrate the feasibility of devised ETIC strategy.

Suggested Citation

  • Xia, Mingli & Liu, Linna & Fang, Jianyin & Qu, Boyang, 2024. "Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003886
    DOI: 10.1016/j.chaos.2024.114836
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    References listed on IDEAS

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    1. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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    5. Liu, Bin & Sun, Zhijie & Luo, Yihao & Zhong, Yuxuan, 2019. "Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    6. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
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