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Finite-time H∞ static output control of Markov jump systems with an auxiliary approach

Author

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  • Shen, Mouquan
  • Yan, Shen
  • Zhang, Guangming
  • Park, Ju H.

Abstract

This paper considers the finite-time H∞ static output feedback control of Markov jump systems. With the help of introducing two new variables related to the original system state and output, sufficient conditions for the closed-loop system to be stochastic finite-time boundedness with the prescribed H∞ performance level are proposed in terms of linear matrix inequalities (LMIs). Meanwhile, the static output control gains are solved explicitly by the proposed conditions. It is shown that the proposed method is less or at least the same conservative than the existing result. Lastly, a numerical example is given to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:553-561
    DOI: 10.1016/j.amc.2015.10.038
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    Cited by:

    1. Zhang, Zhi-Ming & He, Yong & Wu, Min & Wang, Qing-Guo, 2017. "Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 121-132.
    2. Yi, Chengbo & Feng, Jianwen & Wang, Jingyi & Xu, Chen & Zhao, Yi, 2017. "Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 78-90.
    3. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    4. Luo, Jinnan & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Chen, Hao & Gu, Xian-Ming & Wang, Wenqin, 2017. "Non-fragile asynchronous H∞ control for uncertain stochastic memory systems with Bernoulli distribution," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 109-128.
    5. 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.
    6. Liu Xikui & Teng Yapeng & Li Yan, 2020. "Finite-Time H ∞ Static Output Feedback Control for Itô Stochastic Markovian Jump Systems," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    7. Zhou, Ya & Wan, Xiaoxiao & Huang, Chuangxia & Yang, Xinsong, 2020. "Finite-time stochastic synchronization of dynamic networks with nonlinear coupling strength via quantized intermittent control," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    8. Gao, Rui & Zhai, Ding & Cheng, Jun, 2019. "Decentralized static output feedback sliding mode control for interconnected descriptor systems via linear sliding variable," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 185-198.
    9. 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).
    10. Ye, Dan & Yang, Xiang & Su, Lei, 2017. "Fault-tolerant synchronization control for complex dynamical networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 36-48.
    11. Chen, Jian & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2017. "Mixed H∞ and passive control for singular systems with time delay via static output feedback," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 244-253.
    12. 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.
    13. 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.
    14. 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.
    15. Cheng, Jun & Chen, Shiqiang & Liu, Zhijun & Wang, Hailing & Li, Jin, 2016. "Robust finite-time sampled-data control of linear systems subject to random occurring delays and its application to Four-Tank system," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 55-76.
    16. Liang, Kun & Dai, Mingcheng & Shen, Hao & Wang, Jing & Wang, Zhen & Chen, Bo, 2018. "L2−L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 450-462.
    17. Sakthivel, R. & Joby, Maya & Wang, Chao & Kaviarasan, B., 2018. "Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 425-436.
    18. Hyun Kim, Sung, 2019. "Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 542-556.
    19. Li, Lei & Qi, Wenhai & Chen, Xiaoming & Kao, Yonggui & Gao, Xianwen & Wei, Yunliang, 2018. "Stability analysis and control synthesis for positive semi-Markov jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 363-375.
    20. Gu, Yang & Shen, Mouquan & Ren, Yuesheng & Liu, Hongxia, 2020. "H∞ finite-time control of unknown uncertain systems with actuator failure," Applied Mathematics and Computation, Elsevier, vol. 383(C).

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