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Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback

Author

Listed:
  • Wang, Jing
  • Liang, Kun
  • Huang, Xia
  • Wang, Zhen
  • Shen, Hao

Abstract

This paper focuses on the analysis and design of dissipativity-based fault-tolerant controller for discrete-time nonlinear Markov jump singularly perturbed systems (MJSPSs) which are based on Takagi–Sugeno fuzzy model. A novel strategy is proposed to improve the upper bound of singular perturbation parameter (SPP) ϵ, and the fault-tolerant design is also introduced, namely the susceptible property of systems is made full consideration, to ensure the specified performance of a system. The aim is to design an optimized slow state feedback controller such that the stability of MJSPSs is guaranteed even in faulty case, and the upper bound of the SPP ϵ is improved simultaneously. Utilizing Lyapunov functional technique, a sufficient condition for the existence of controller is shown. Last but not least, the control issue of a series DC motor model as an illustrated example is given to explain the availability of the presented design scheme.

Suggested Citation

  • Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:247-262
    DOI: 10.1016/j.amc.2018.01.049
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    References listed on IDEAS

    as
    1. 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.
    2. Su, Lei & Shen, Hao, 2015. "Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 931-942.
    3. 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.
    4. Zhou, Jianping & Sang, Chengyan & Li, Xiao & Fang, Muyun & Wang, Zhen, 2018. "H∞ consensus for nonlinear stochastic multi-agent systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 41-58.
    5. 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.
    6. 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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