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Exponential stability of switched systems with state-dependent delayed impulses via B-equivalent method

Author

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  • Cui, Qian
  • Cao, Jinde
  • Li, Lulu
  • Liu, Yang

Abstract

This paper studies the stability problem of switched systems with state-dependent delayed impulses (SDDIs), where switching times satisfy the definition of average dwell-time. Firstly, the pulse phenomenon of the systems with SDDIs is avoided under some necessary assumptions. Subsequently, the state-dependent delayed impulsive switched systems can be transformed into the corresponding time-dependent ones by using the B-equivalent method. Furthermore, the stability of stable and unstable systems with time-dependent delayed impulses (TDDIs) are analyzed, where the limitation that the impulsive delays are less than the impulsive intervals is relaxed. Based on the equivalence of the original system and the corresponding switched system with TDDIs, some new stability conditions for the switched systems with SDDIs are derived. Finally, the theoretical results are applied to a switched neural network with SDDIs to demonstrate the validity of the results.

Suggested Citation

  • Cui, Qian & Cao, Jinde & Li, Lulu & Liu, Yang, 2025. "Exponential stability of switched systems with state-dependent delayed impulses via B-equivalent method," Applied Mathematics and Computation, Elsevier, vol. 486(C).
    • Handle: RePEc:eee:apmaco:v:486:y:2025:i:c:s0096300324004922
    DOI: 10.1016/j.amc.2024.129031
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    References listed on IDEAS

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    1. Yang, Huilan & Wang, Xin & Zhong, Shouming & Shu, Lan, 2018. "Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 75-85.
    2. He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Yao, Meng & Wei, Guoliang & Guo, Xinchen, 2024. "Input-to-state stabilization of networked impulsive systems under communication constraints: A refined Lyapunov functional," Applied Mathematics and Computation, Elsevier, vol. 463(C).
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