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Lyapunov conditions for finite-time stability of disturbed nonlinear impulsive systems

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  • Xing, Ying
  • He, Xinyi
  • Li, Xiaodi

Abstract

What we concern in this paper is finite-time control of nonlinear impulsive systems involving external disturbance, where practical finite-time and finite-time stabilization are studied with respect to nonvanishing and vanishing disturbance, respectively. A relationship between the finite settling time and the impulsive frequency is presented to show the stabilizing effect of impulses. It is shown that systems subject to nonvanishing disturbance can enter a disturbance-dependent ultimate bound in a finite-time sense, and a relatively smaller bound of settling time is obtained by utilizing stabilizing impulses. Meanwhile, systems subject to vanishing disturbance can achieve finite-time stabilization at the origin. Moreover, compared with the situation without impulses, the corresponding bound of settling time is also smaller. For the sake of illustrating the validity of proposed results, some examples and their simulations are provided.

Suggested Citation

  • Xing, Ying & He, Xinyi & Li, Xiaodi, 2023. "Lyapunov conditions for finite-time stability of disturbed nonlinear impulsive systems," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007366
    DOI: 10.1016/j.amc.2022.127668
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    References listed on IDEAS

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    1. He, Xiaoyan & Wang, Qingyun & Yu, Wenwu, 2015. "Finite-time distributed cooperative attitude tracking control for multiple rigid spacecraft," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 724-734.
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    3. Zengyun Wang & Jinde Cao & Zuowei Cai & Changfeng Xue, 2021. "A novel fixed-time stability of nonlinear impulsive systems: a two-stage comparison principle method," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(10), pages 2114-2128, July.
    4. Wu, Jie & He, Xinyi & Li, Xiaodi, 2022. "Finite-time stabilization of time-varying nonlinear systems based on a novel differential inequality approach," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    5. Zhou, Wenjia & Hu, Yuanfa & Liu, Xiaoyang & Cao, Jinde, 2022. "Finite-time adaptive synchronization of coupled uncertain neural networks via intermittent control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
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    1. 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).

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