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A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities

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  • Shen, Mouquan
  • Ye, Dan

Abstract

This paper is concerned with the state feedback control of continuous Markov jump linear systems with incomplete transition probabilities in finite frequency domain. By developing a new technique to handle the coupling among Lyapunov variable, system matrix and controller parameter, new sufficient conditions for the closed-loop system to be stochastically stable with the required finite frequency performance are established in terms of linear matrix inequalities. Meanwhile, the finite frequency state feedback controller is also obtained by the proposed conditions directly. The validity of the proposed method is demonstrated by a numerical example.

Suggested Citation

  • Shen, Mouquan & Ye, Dan, 2017. "A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 53-64.
    • Handle: RePEc:eee:apmaco:v:295:y:2017:i:c:p:53-64
    DOI: 10.1016/j.amc.2016.09.024
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    References listed on IDEAS

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    1. Li, Feng & Shen, Hao & Chen, Mengshen & Kong, Qingkai, 2015. "Non-fragile finite-time l2−l∞ state estimation for discrete-time Markov jump neural networks with unreliable communication links," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 467-481.
    2. Sakthivel, R. & Saravanakumar, T. & Kaviarasan, B. & Marshal Anthoni, S., 2016. "Dissipativity based repetitive control for switched stochastic dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 340-353.
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    4. Zhao, Huanyu & Park, Ju H. & Zhang, Yulin, 2014. "Couple-group consensus for second-order multi-agent systems with fixed and stochastic switching topologies," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 595-605.
    5. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
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    Cited by:

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    2. 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.
    3. Lee, Tae H. & Park, Ju H. & Jung, Hoyoul, 2018. "Network-based H∞ state estimation for neural networks using imperfect measurement," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 205-214.
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    5. 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).
    6. 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.
    7. 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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