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Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints

Author

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  • Chen, Mengshen
  • Yang, Xiaofei
  • Shen, Hao
  • Yao, Fengqi

Abstract

This paper is concerned with the problem of finite-time H∞ control for Markov jump repeated scalar nonlinear systems (MJRSNSs) with input constraints. The jumps between MJRSNSs and desired mode-dependent controllers are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the different degrees of asynchronous jumps between MJRSNSs and controllers. With the aid of Lyapunov–Krasovskii methodology, some H∞ performance criteria for the MJRSNSs are proposed. Based on these criteria, sufficient conditions on the existence of the desired controllers are established, and then the gains of the controllers can be obtained by solving a convex optimization problem. Finally, an example is presented to illustrate the effectiveness of our method.

Suggested Citation

  • Chen, Mengshen & Yang, Xiaofei & Shen, Hao & Yao, Fengqi, 2016. "Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 172-180.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:172-180
    DOI: 10.1016/j.amc.2015.11.070
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    References listed on IDEAS

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    1. Mathiyalagan, K. & Park, Ju H. & Sakthivel, R., 2015. "Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 967-979.
    2. Jun Cheng & Hong Zhu & Shouming Zhong & Yuping Zhang & Yuanyuan Li, 2015. "Finite-time control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 1080-1093, April.
    3. Gang Gao & Jinzhi Wang & Xianghua Wang, 2014. "Robust tracking control for an air-breathing hypersonic vehicle with input constraints," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 2466-2479, December.
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    Citations

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    Cited by:

    1. Song, Xiaona & Men, Yunzhe & Zhou, Jianping & Zhao, Junjie & Shen, Hao, 2017. "Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 123-132.
    2. 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.
    3. Lin, Xiangze & Zhang, Wanli & Huang, Shuaiting & Zheng, Enlai, 2020. "Finite-time stabilization of input-delay switched systems," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    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. 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.
    6. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.
    7. Lin, Xiangze & Li, Shihua & Zou, Yun, 2017. "Finite-time stabilization of switched linear time-delay systems with saturating actuators," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 66-79.
    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.

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