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Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems

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  • Zhao, Ping
  • Feng, Wei
  • Zhao, Yan
  • Kang, Yu

Abstract

In this paper, the problems of finite-time globally asymptotical stability in probability (FGSP) and finite-time stochastic input-to-state stability (FSISS) for switched stochastic nonlinear (SSNL) systems are investigated. To solve these problems elegantly, some new definitions on FGSP and FSISS are presented in the form of generalized KL (GKL) function, and some lemmas about GKL functions and their properties are proved. Based on that, some sufficient conditions are provided firstly for nonswitched stochastic nonlinear (nSSNL) systems, which will make the corresponding study on SSNL systems easier. Then, overcoming the difficulties coming with the appearance of switching, some sufficient conditions on FGSP and FSISS are given for SSNL systems. Moreover, based on the concept of average dwell-time, a sufficient condition for FSISS of SSNL systems is also provided. Finally, some simulation examples are given to demonstrate the effectiveness of our results.

Suggested Citation

  • Zhao, Ping & Feng, Wei & Zhao, Yan & Kang, Yu, 2015. "Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1038-1054.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:1038-1054
    DOI: 10.1016/j.amc.2015.06.075
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    References listed on IDEAS

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    1. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Su, Qingyu & Jia, Xiaolong & Liu, Honghai, 2016. "Finite-time stabilization of a class of cascade nonlinear switched systems under state-dependent switching," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 172-180.
    2. Zhang, Meng & Zhu, Quanxin, 2022. "Finite-time input-to-state stability of switched stochastic time-varying nonlinear systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Wang, Yijing & Zou, Yanchao & Zuo, Zhiqiang & Li, Hongchao, 2016. "Finite-time stabilization of switched nonlinear systems with partial unstable modes," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 172-181.

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