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Stability analysis of semi-Markov switching stochastic mode-dependent delay systems with unstable subsystems

Author

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  • Xiao, Hanni
  • Zhu, Quanxin
  • Karimi, Hamid Reza

Abstract

This paper is dedicated to studying the stability of semi-Markov switching stochastic delay systems with unstable subsystems, where delay depends on another semi-Markovian process and transition rates are uncertain. Based on the stochastic analysis theory and the mode-dependent multi-Lyapunov function method, relevant sufficient conditions are established to ensure the asymptotic stability in mean square of the system. In addition, contrary to the existing works, the system under consider is more general and our works are not only applicable to the system with partial unstable subsystems, but also applicable to the system with all unstable subsystems. Finally, one numerical example is provided to illustrate the correctness of the method described in the paper.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009705
    DOI: 10.1016/j.chaos.2022.112791
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    References listed on IDEAS

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    1. Li, Guangjie & Yang, Qigui, 2021. "Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Caraballo, Tomás & Belfeki, Mohsen & Mchiri, Lassaad & Rhaima, Mohamed, 2021. "h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Pan, Suying & Zhou, Jin & Ye, Zhiyong, 2021. "Event-triggered dynamic output feedback control for networked Markovian jump systems with partly unknown transition rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 539-561.
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    Cited by:

    1. Ma, Yajing & Li, Zhanjie & Xie, Xiangpeng & Yue, Dong, 2023. "Adaptive consensus of uncertain switched nonlinear multi-agent systems under sensor deception attacks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Guo, Beibei & Xiao, Yu, 2023. "Intermittent synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump and its application of Chua’s circuits," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. 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).

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