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Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative

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  • Peng Li
  • Xiaodi Li
  • Jinde Cao

Abstract

This paper studies the input-to-state stability (ISS) of nonlinear switched systems. By using Lyapunov method involving indefinite derivative and average dwell-time (ADT) method, some sufficient conditions for ISS are obtained. In our approach, the time-derivative of the Lyapunov function is not necessarily negative definite and that allows wider applications than existing results in the literature. Examples are provided to illustrate the applications and advantages of our general results and the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:8701219
    DOI: 10.1155/2018/8701219
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    References listed on IDEAS

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    1. 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.
    2. Chongyang Liu & Zhaohua Gong & Enmin Feng & Hongchao Yin, 2012. "Optimal switching control of a fed-batch fermentation process," Journal of Global Optimization, Springer, vol. 52(2), pages 265-280, February.
    3. 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.
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    Cited by:

    1. 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.
    2. Li, Mingyue & Chen, Huanzhen & Li, Xiaodi, 2021. "Exponential stability of nonlinear systems involving partial unmeasurable states via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Hamza Khan & József K. Tar & Imre Rudas & Levente Kovács & György Eigner, 2018. "Receding Horizon Control of Type 1 Diabetes Mellitus by Using Nonlinear Programming," Complexity, Hindawi, vol. 2018, pages 1-11, April.
    4. Yang, Xueyan & Peng, Dongxue & Lv, Xiaoxiao & Li, Xiaodi, 2019. "Recent progress in impulsive control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 244-268.

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