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Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching

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  • Gao, Xianwen
  • He, Hangfeng
  • Qi, Wenhai

Abstract

This paper deals with admissibility analysis for discrete-time singular Markov jump systems (SMJSs) with asynchronous switching, which means the switching of controllers is asynchronous with the switching of subsystems. The switching delay and state delay are modeled as Markov chains. The resulting closed-loop system is modeled as a singular system with a Markovian jumping vector and two Markovian jumping parameters. A new necessary and sufficient condition for regularity, causality and stability of the closed-loop system is proposed. Based on this, a state feedback controller is designed in terms of a strict linear matrix inequality (LMI) to guarantee the admissibility of SMJSs with asynchronous switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Suggested Citation

  • Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:431-441
    DOI: 10.1016/j.amc.2017.06.001
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    References listed on IDEAS

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    8. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.
    9. Qi, Wenhai & Gao, Xianwen, 2016. "H∞ observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 80-97.
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    12. 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.
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    Cited by:

    1. Yu, Peng & Ma, Yuechao, 2020. "Observer-based asynchronous control for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    2. Xu, Qiyi & Zhang, Yijun & Qi, Wenhai & Xiao, Shunyuan, 2020. "Event-triggered mixed H∞ and passive filtering for discrete-time networked singular Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    3. Vargas, Alessandro N. & Montezuma, Marcio A.F. & Liu, Xinghua & Oliveira, Ricardo C.L.F., 2019. "Robust stability of Markov jump linear systems through randomized evaluations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 287-294.

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