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Local finite-time input-to-state stability of impulsive systems with unstable jumps

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  • Xi, Qiang
  • Liu, Xinzhi
  • Xia, Jianwei

Abstract

This article investigates the local finite-time input-to-state stability of impulsive systems with unstable jumps, an extended concept proposed for impulsive systems for the first time. The main results are obtained by employing a comparison principle, which reduce the local finite-time input-to-state stability of the original system to the local finite-time stability of a scalar impulsive system. The scalar system is constructed based on a key assumption involving a relaxed differential inequality of Lyapunov function. Another major result is a theorem on local finite-time stability of the scalar impulsive system with unstable jumps, which provides the domain of attraction, initial-value-dependent minimum dwell-time, and settling time estimation. Two examples with simulations are provided to validate the theoretical results.

Suggested Citation

  • Xi, Qiang & Liu, Xinzhi & Xia, Jianwei, 2026. "Local finite-time input-to-state stability of impulsive systems with unstable jumps," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017795
    DOI: 10.1016/j.chaos.2025.117765
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    References listed on IDEAS

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    1. Jiang, Tong & Xing, Ying & Li, Xiaodi, 2025. "Finite-time stability of time-varying systems involving multiple impulses and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    2. He, Xinyi & Li, Xiaodi & Nieto, Juan J., 2021. "Finite-time stability and stabilization for time-varying systems," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. 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).
    4. Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Hui Zhao & Jingfeng Ren, 2016. "Finite-time synchronization of complex dynamical networks with multi-links via intermittent controls," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-12, February.
    5. Xie, Liheng & Liu, Shutang & Zhu, Xingao, 2025. "Prescribed-time stability of stochastic nonlinear delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    6. Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Hui Zhao & Jingfeng Ren, 2016. "Finite-time synchronization of complex dynamical networks with multi-links via intermittent controls," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-12, February.
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