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Stability of nonlinear delayed impulsive control systems via step-function method

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  • Wang, Yinuo
  • Li, Chuandong
  • Wu, Hongjuan
  • Deng, Hao

Abstract

In this paper, considering that the limited speed of information transfer may generate time delay, which can sometimes influence the stability of the system, but in reality time delay is pervasive, and sometimes can have a positive impact on system’s stability, so it is essential to think about its existence. The nonlinear systems under delayed impulsive control (IC) are investigated here, and we mainly utilize the multiple-spans step-function method to analyse the stability conditions of the considered systems, which can be counted as a generalization of the Lyapunov-like stability method and is less conservative compared with the existing traditional Lyapunov-like function method. Moreover, it is the first time that this method employed for the stability of systems with IC and time delay. Two examples of equidistant impulses of nonlinear autonomous system and non-equidistant impulses of linear time-varying system by using two-spans step-function method are presented to validate the utility of the presented approach, respectively. Besides, the Zeno behavior of autonomous system without time delay is provided and treated by the presented method, which can better manifest the extensive viability of the method compared with the Lyapunov-like function method.

Suggested Citation

  • Wang, Yinuo & Li, Chuandong & Wu, Hongjuan & Deng, Hao, 2024. "Stability of nonlinear delayed impulsive control systems via step-function method," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011834
    DOI: 10.1016/j.chaos.2024.115631
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    References listed on IDEAS

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    1. Yang, Xinsong & Huang, Chuangxia & Zhu, Quanxin, 2011. "Synchronization of switched neural networks with mixed delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 817-826.
    2. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
    3. Huan, Mingchen & Li, Chuandong, 2022. "Stability analysis of state-dependent impulsive systems via a new two-sided looped functional," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Fang, Qi & Wang, Mingzhu & Li, Xiaodi, 2023. "Event-triggered distributed delayed impulsive control for nonlinear systems with applications to complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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    1. He, Haibin & Jiang, Nan & Liu, Xiaoyang & Fan, Lu & Cao, Jinde, 2025. "Impulsive synchronization and parameter optimization for disturbed inertial memristive neural networks with actuator saturation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).

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