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Input-to-state-KL-stability and criteria for a class of hybrid dynamical systems

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  • Liu, Bin
  • Hill, David J.
  • Sun, Zhijie

Abstract

This paper aims to study input-to-state-KL-stability (IS-KL-stability) for a class of hybrid dynamical systems (HDS). The notions of IS-KLK0-property and IS-KL-stability are proposed. The IS-KLK0-property, including input-to-state stability (ISS), IS-KL-stability, and some non-ISS property, is a more general input-to-state property and reflects the specific effects on the dynamic behaviors from the dynamics of subsystems, switching events, and external inputs in HDS. An HDS with IS-KLK0-property is allowed to have non-ISS property. The criteria of IS-KL-stability are established for HDS with IS-KLK0-property subsystems via introducing a hybrid dwell time condition. The hybrid dwell time condition unifies the often used average dwell-time condition and converse average dwell-time condition. Moreover, the criteria on IS-KL-stability including event-ISS are established by the method of multiple Lyapunov-like functions. Finally, two examples are provided to verify the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:326:y:2018:i:c:p:124-140
    DOI: 10.1016/j.amc.2018.01.002
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    Cited by:

    1. Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.
    2. 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.
    3. Li, Yuanen & Zhang, Huasheng & Zhang, Tingting & Geng, Han, 2023. "Interval stability/stabilization and H∞ feedback control for linear impulsive stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    4. 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.
    5. Long, Mingkang & Su, Housheng & Liu, Bo, 2019. "Second-order controllability of two-time-scale multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 299-313.
    6. Jinlong Yuan & Jun Xie & Honglei Xu & Enmin Feng & Zhilong Xiu, 2019. "Optimization for Nonlinear Uncertain Switched Stochastic Systems with Initial State Difference in Batch Culture Process," Complexity, Hindawi, vol. 2019, pages 1-15, February.
    7. Li, Jinghan & Zhao, Jun, 2022. "Bumpless transfer based event-triggered control for switched linear systems with state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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