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Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations

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  • Yongbao Wu
  • Wenxue Li
  • Jiqiang Feng

Abstract

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results.

Suggested Citation

  • Yongbao Wu & Wenxue Li & Jiqiang Feng, 2017. "Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(13), pages 2850-2859, October.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:13:p:2850-2859
    DOI: 10.1080/00207721.2017.1344892
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    Citations

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    Cited by:

    1. Xu, Yao & Chu, Chenyin & Li, Wenxue, 2018. "Quantized feedback control scheme on coupled systems with time delay and distributed delay: A finite-time inner synchronization analysis," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 315-328.
    2. Zhenyu Zhu & Zhanshan Zhao & Haoliang Cui & Fengdong Shi, 2019. "Improved T-S Fuzzy Control for Uncertain Time-Delay Coronary Artery System," Complexity, Hindawi, vol. 2019, pages 1-11, May.
    3. Liu, Yan & Mei, Jingling & Li, Wenxue, 2018. "Stochastic stabilization problem of complex networks without strong connectedness," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 304-315.
    4. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    5. Liu, Yan & Yu, Pinrui & Chu, Dianhui & Su, Huan, 2019. "Stationary distribution of stochastic Markov jump coupled systems based on graph theory," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 188-195.

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