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H∞ control of Markov jump systems with time-varying delay and incomplete transition probabilities

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  • Li, Lingchun
  • Shen, Mouquan
  • Zhang, Guangming
  • Yan, Shen

Abstract

This paper addresses the H∞ control of continuous Markov jump systems with interval time-varying delay and incomplete transition probabilities. A linearization method is used to handle unknown transition probabilities. Meanwhile, the Wirtinger-based integral inequality and the reciprocally convex technique are adopted to deal with the time-varying delay. Additionally, a separating technique is employed to tackle the coupling among Lyapunov variable, system matrix and controller parameter. Based on these strategies, new sufficient conditions for the closed-loop system to be stochastically stable are formulated in the framework of linear matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Li, Lingchun & Shen, Mouquan & Zhang, Guangming & Yan, Shen, 2017. "H∞ control of Markov jump systems with time-varying delay and incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 95-106.
    • Handle: RePEc:eee:apmaco:v:301:y:2017:i:c:p:95-106
    DOI: 10.1016/j.amc.2016.12.027
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    References listed on IDEAS

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    1. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
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    3. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
    4. Feng, Zhiguang & Li, Wenxing & Lam, James, 2015. "New admissibility analysis for discrete singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1058-1066.
    5. Zhang, Yingqi & Shi, Yan & Shi, Peng, 2016. "Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 125-138.
    6. Rajavel, S. & Samidurai, R. & Cao, Jinde & Alsaedi, Ahmed & Ahmad, Bashir, 2017. "Finite-time non-fragile passivity control for neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 145-158.
    7. Yanling Wei & Jianbin Qiu & Hamid Reza Karimi & Mao Wang, 2014. "model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1496-1507, July.
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    Cited by:

    1. 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.
    2. Aravindh, D. & Sakthivel, R. & Kong, Fanchao & Marshal Anthoni, S., 2020. "Finite-time reliable stabilization of uncertain semi-Markovian jump systems with input saturation," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    3. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    4. Song, Xiaona & Wang, Mi & Song, Shuai & Wang, Zhen, 2019. "Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 371-395.

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