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Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative

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  • Li, Peng
  • Li, Xiaodi

Abstract

This paper investigates the input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained, where both types of impulses, stabilizing impulses and destabilizing impulses, are considered. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite, that allows wider applications than existing results in the literature. Several illustrative examples are presented, with their numerical simulations, to demonstrate the main results.

Suggested Citation

  • Li, Peng & Li, Xiaodi, 2019. "Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 314-323.
    • Handle: RePEc:eee:matcom:v:155:y:2019:i:c:p:314-323
    DOI: 10.1016/j.matcom.2018.06.010
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    References listed on IDEAS

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    1. Liu, Bin & Hill, David J. & Sun, Zhijie, 2018. "Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 124-140.
    2. Ning, Chongyang & He, Yong & Wu, Min & Zhou, Shaowu, 2015. "Indefinite derivative Lyapunov–Krasovskii functional method for input to state stability of nonlinear systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 534-542.
    3. Peng Li & Xiaodi Li & Jinde Cao, 2018. "Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative," Complexity, Hindawi, vol. 2018, pages 1-8, January.
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    Cited by:

    1. Wang, Yaqi & Lu, Jianquan & Cao, Jinde & Huang, Wei & Guo, Jianhua & Wei, Yun, 2020. "Input-to-state stability of the road transport system via cyber–physical optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 3-12.

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