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Stability of stochastic systems with semi-Markovian switching and impulses

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  • Chen, Feng
  • Chen, Yuming
  • Zhu, Quanxin
  • Zhang, Qimin

Abstract

The aim of this paper is to investigate the stochastic asymptotic stability of semi-Markov switched systems with mixed impulses. A novel definition of average impulse gain is given to estimate the intensity of the mixed impulses. Based on the multiple Lyapunov function approach and average impulse interval method, we provide sufficient conditions on the stochastic asymptotic stability for the semi-Markov switched system with impulses. Moreover, the influence of impulses on the system is estimated by applying the average impulse gain and average impulse interval method, which are not only suitable for synchronous impulses but also for asynchronous impulses. The theoretical results are demonstrated by two examples.

Suggested Citation

  • Chen, Feng & Chen, Yuming & Zhu, Quanxin & Zhang, Qimin, 2023. "Stability of stochastic systems with semi-Markovian switching and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011499
    DOI: 10.1016/j.chaos.2023.114247
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    References listed on IDEAS

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    1. Xiao, Hanni & Zhu, Quanxin & Karimi, Hamid Reza, 2022. "Stability analysis of semi-Markov switching stochastic mode-dependent delay systems with unstable subsystems," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Jianhua Wang & Qingling Zhang & Xiaoxu Liu, 2015. "control for discrete-time singular Markovian jump systems based on the novel bounded real lemma," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(1), pages 63-75, January.
    3. Ye, Dan & Yang, Xiang & Su, Lei, 2017. "Fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 36-48.
    4. Cemil Tunç, 2005. "On the asymptotic behavior of solutions of certain third-order nonlinear differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 2005, pages 1-7, January.
    5. Yu Zhang & Cheng Wang, 2015. "Robust stochastic stability of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2210-2220, September.
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