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Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case

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  • Hu, Jun
  • Zhang, Panpan
  • Kao, Yonggui
  • Liu, Hongjian
  • Chen, Dongyan

Abstract

This paper studies the sliding-mode-based control problem for a class of delayed Markovian jump repeated scalar nonlinear systems (RSNSs) subject to packet dropouts (PDs) and randomly occurring uncertainties (ROUs). Here, the phenomenon of the Markovian PDs is modeled by utilizing a random variable obeying Markov process. By using the Bernoulli distributed random variables, the ROUs under uncertain occurrence probabilities (UOPs) are characterized from the mathematical perspective. In addition, the time-delay considered is bounded time-varying with known upper and lower bounds. The attention is on designing a sliding-mode-based control method for Markovian jump RSNSs in the simultaneous presence of Markovian PDs, ROUs and time-varying delays. Specifically, the robustly asymptotically mean-square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion. Moreover, the reachability in discrete setting is analyzed, i.e., the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre-designed sliding surface in mean square sense by synthesizing a robust sliding mode control (SMC) law. Finally, the effectiveness of developed control method is verified by some simulations.

Suggested Citation

  • Hu, Jun & Zhang, Panpan & Kao, Yonggui & Liu, Hongjian & Chen, Dongyan, 2019. "Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:33
    DOI: 10.1016/j.amc.2019.124574
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    References listed on IDEAS

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    1. Chen, Xiangyong & Park, Ju H. & Cao, Jinde & Qiu, Jianlong, 2017. "Sliding mode synchronization of multiple chaotic systems with uncertainties and disturbances," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 161-173.
    2. Gao, Rui & Zhai, Ding & Cheng, Jun, 2019. "Decentralized static output feedback sliding mode control for interconnected descriptor systems via linear sliding variable," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 185-198.
    3. Yueqiao Han & Yonggui Kao & Cunchen Gao & Baoping Jiang, 2017. "Robust sliding mode control for uncertain discrete singular systems with time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 818-827, March.
    4. Yan, Zhiguo & Park, Ju H. & Zhang, Weihai, 2018. "A unified framework for asymptotic and transient behavior of linear stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 31-40.
    5. Chu, Xiaoan & Li, Muguo, 2019. "Observer-based model following sliding mode tracking control of discrete-time linear networked systems with two-channel event-triggered schemes and quantizations," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 428-448.
    6. 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.
    7. Deqiang Zeng & Ruimei Zhang & Xinzhi Liu & Shouming Zhong & Kaibo Shi, 2018. "Improved results on synchronisation of delayed complex dynamical networks via sampled-data control," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(6), pages 1242-1255, April.
    8. Zhou, Qi & Yao, Deyin & Wang, Jiahui & Wu, Chengwei, 2016. "Robust control of uncertain semi-Markovian jump systems using sliding mode control method," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 72-87.
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    Cited by:

    1. Haifeng Huang & Mohammadamin Shirkhani & Jafar Tavoosi & Omar Mahmoud, 2022. "A New Intelligent Dynamic Control Method for a Class of Stochastic Nonlinear Systems," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    2. Mengmeng Sun & Dongyan Chen, 2019. "Robust Protocol-Based Consensus Control of Time-Varying Uncertain Multiagent Systems Subject to Missing Measurements," Complexity, Hindawi, vol. 2019, pages 1-13, November.

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