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Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems

Author

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  • Wang, Jimin
  • Ma, Shuping
  • Zhang, Chenghui

Abstract

This paper investigates the stochastic stability and the state feedback control design for a class of nonlinear continuous-time descriptor semi-Markov jump systems whose transition rates are time-varying, which are more general than the descriptor Markov jump systems. First, by deriving the infinitesimal generator for stochastic Lyapunov functional of descriptor semi-Markov jump systems, a stochastic stability condition is established, which guarantees this kind of systems are regular, impulse-free, have a unique solution, and are stochastically stable. In order to design the state feedback controller, a linear matrix inequality (LMI) stability condition is developed based on the lower and upper bounds of the time-varying transition probability and singular value decomposition approach. Furthermore, the state feedback controller design is developed in terms of LMI approach. Last, numerical examples are given to demonstrate the effectiveness of the obtained methods.

Suggested Citation

  • Wang, Jimin & Ma, Shuping & Zhang, Chenghui, 2016. "Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 90-102.
    • Handle: RePEc:eee:apmaco:v:279:y:2016:i:c:p:90-102
    DOI: 10.1016/j.amc.2016.01.013
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    Citations

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    Cited by:

    1. Ren, Junchao & Feng, Lihong & Fu, Jun & Zhuang, Tianyu, 2021. "Admissibility analysis and passive output feedback control for one-sided Lipschitz nonlinear singular Markovian jump systems with uncertainties," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Gao, Meng & Zhang, Lihua & Qi, Wenhai & Cao, Jinde & Cheng, Jun & Kao, Yonggui & Wei, Yunliang & Yan, Xiaoyu, 2020. "SMC for semi-Markov jump T-S fuzzy systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    4. Xu, Tianbo & Gao, Xianwen & Qi, Wenhai & Wei, Yunliang, 2019. "Disturbance-observer-based control for semi-Markovian jump systems with generally uncertain transition rate and saturation nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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