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Robust sliding mode control for Markovian jump singular systems with randomly changing structure

Author

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  • Zhao, Wenying
  • Ma, Yuechao
  • Chen, Aihong
  • Fu, Lei
  • Zhang, Yutong

Abstract

This paper discusses the robust optimization by a sliding mode control (SMC) approach for uncertain singular Markovian jump (SMJ) time-varying delay system with nonlinear perturbation, which uncertainties occur randomly. Firstly, a different integral-type sliding mode surface (SMS) and a different Lyapunov–Krasovskii function are introduced. Secondly, by using linear matrix inequalities, sufficient conditions are proposed to ensure the mean-square exponentially admissible (MSEA) with an H∞ performance level γ of the unforced uncertain SMJ time-varying delay system in the specified SMS. Next, a composed SMC law with the parameter uncertainties occurring randomly can ensure the reachability of the predefined SMS. Finally, three numerical examples are given to test the feasibility of the theory.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:81-96
    DOI: 10.1016/j.amc.2018.12.014
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    References listed on IDEAS

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    1. Liu, Yangfan & Ma, Yuechao & Wang, Yanning, 2018. "Reliable finite-time sliding-mode control for singular time-delay system with sensor faults and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 341-357.
    2. 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.
    3. 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.
    4. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    5. 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.
    6. 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.
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    Cited by:

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    3. Zhao, Yinghong & Ma, Yuechao, 2021. "Asynchronous H∞ control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    4. Xu, Qiyi & Zhang, Yijun & Qi, Wenhai & Xiao, Shunyuan, 2020. "Event-triggered mixed H∞ and passive filtering for discrete-time networked singular Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    5. Sakthivel, Ramalingam & Sakthivel, Rathinasamy & Kwon, Oh-Min & Selvaraj, Palanisamy, 2021. "Disturbance rejection for singular semi-Markov jump neural networks with input saturation," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    6. 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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    8. Kong, Chuifeng & Ma, Yuechao & Liu, Deyou, 2019. "Observer-based quantized sliding mode dissipative control for singular semi-Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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