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Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates

Author

Listed:
  • Jiang, Baoping
  • Gao, Cunchen
  • Kao, Yonggui
  • Liu, Zhen

Abstract

This paper is concerned with robust sliding mode control (SMC) for continuous-time Markovian jump delay systems with incomplete transition rates (TRs), the time-varying delays are unclear and just bounded sometimes. Two methods are employed to investigate this control issue. One is movement decomposition method by which reduced-order sliding mode dynamics is obtained; the other is via sliding mode observer and full-order sliding mode dynamics is obtained on the estimation space. In both cases, sufficient conditions are established in terms of a set of coupled linear matrix inequalities (LMIs) to ensure the sliding mode dynamics to be mean-square exponentially stable; moreover, novel sliding mode controllers, which need not full knowledge on time-varying delays, are synthesized to guarantee the reachability of the prescribed sliding surface. Finally, numerical examples are provided to illustrate the effectiveness of the proposed methods.

Suggested Citation

  • Jiang, Baoping & Gao, Cunchen & Kao, Yonggui & Liu, Zhen, 2016. "Sliding mode control of Markovian jump systems with incomplete information on time-varying delays and transition rates," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 66-79.
    • Handle: RePEc:eee:apmaco:v:290:y:2016:i:c:p:66-79
    DOI: 10.1016/j.amc.2016.05.038
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    References listed on IDEAS

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    1. Liu, Zhen & Gao, Cunchen & Kao, Yonggui, 2015. "Robust H-infinity control for a class of neutral-type systems via sliding mode observer," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 669-681.
    2. Jiang, Baoping & Gao, Cunchen & Xie, Jing, 2015. "Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 187-200.
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    Cited by:

    1. Xue, Yanmei & Zheng, Bo-Chao & Li, Tao & Li, Yuanlu, 2017. "Robust adaptive state feedback sliding-mode control of memristor-based Chua’s systems with input nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 142-153.
    2. Zhao, Wenying & Ma, Yuechao & Chen, Aihong & Fu, Lei & Zhang, Yutong, 2019. "Robust sliding mode control for Markovian jump singular systems with randomly changing structure," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 81-96.
    3. Ran, Suzhen & Xue, Yanmei & Zheng, Bo-Chao & Wang, Zhenyou, 2017. "Quantized feedback fuzzy sliding mode control design via memory-based strategy," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 283-295.
    4. Tao, Ruifeng & Ma, Yuechao & Wang, Chunjiao, 2020. "Stochastic admissibility of singular Markov jump systems with time-delay via sliding mode approach," Applied Mathematics and Computation, Elsevier, vol. 380(C).

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