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Non-fragile H∞ finite-time sliding mode control for stochastic Markovian jump systems with time delay

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  • Zhou, Yaoyao
  • Chen, Gang

Abstract

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.

Suggested Citation

  • Zhou, Yaoyao & Chen, Gang, 2021. "Non-fragile H∞ finite-time sliding mode control for stochastic Markovian jump systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004720
    DOI: 10.1016/j.amc.2021.126383
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    References listed on IDEAS

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    1. Liu, Yu-An & Tang, Shengdao & Liu, Yufan & Kong, Qingkai & Wang, Jing, 2021. "Extended dissipative sliding mode control for nonlinear networked control systems via event-triggered mechanism with random uncertain measurement," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Ma, Yuechao & Jia, Xiaorui & Liu, Deyou, 2016. "Robust finite-time H∞ control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 213-227.
    3. Abdelfettah Hocine & Mohammed Chadli & Hamid Reza Karimi, 2014. "A structured filter for Markovian switching systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1518-1527, July.
    4. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
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    Cited by:

    1. Li, Jiajia & Tian, Xin & Wei, Guoliang, 2022. "Asynchronous partially mode-dependent control for switched larger-scale nonlinear systems with bounded sojourn time," Applied Mathematics and Computation, Elsevier, vol. 418(C).

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