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Finite-time stabilization of stochastic coupled systems on networks with Markovian switching via feedback control

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  • Wu, Yongbao
  • Guo, Haihua
  • Li, Wenxue

Abstract

This paper is concerned with the finite-time stabilization issue of stochastic coupled systems on networks with Markovian switching via feedback control. The aim of this paper is to design a state feedback controller to stabilize the states of such stochastic coupled systems on networks within finite time. Focusing on the finite-time stabilization issue, this paper utilizes Kirchhoff’s Matrix Tree Theorem and Lyapunov method to establish two sufficient criteria. Based on these criteria, the relationship between the time to reach finite-time stabilization and the topology structure of the network can be shown. Furthermore, to verify our theoretical results, an application to a concrete finite-time stabilization problem of stochastic coupled oscillators with Markovian switching is presented. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed results.

Suggested Citation

  • Wu, Yongbao & Guo, Haihua & Li, Wenxue, 2020. "Finite-time stabilization of stochastic coupled systems on networks with Markovian switching via feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315869
    DOI: 10.1016/j.physa.2019.122797
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    References listed on IDEAS

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    1. Yu, Jingyi & Liu, Meng, 2017. "Stationary distribution and ergodicity of a stochastic food-chain model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 14-28.
    2. Zhang, Chunmei & Chen, Tianrui, 2018. "Exponential stability of stochastic complex networks with multi-weights based on graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 602-611.
    3. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
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    Cited by:

    1. Cheng Peng & Jiaxin Ma & Qiankun Li & Shang Gao, 2022. "Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    2. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    3. Zou, Cong & Li, Bing & Liu, Feiyang & Xu, Bingrui, 2022. "Event-Triggered μ-state estimation for Markovian jumping neural networks with mixed time-delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Jiang, Tingting & Zhang, Yuping & Zeng, Yong & Zhong, Shouming & Shi, Kaibo & Cai, Xiao, 2021. "Finite-time analysis for networked predictive control systems with induced time delays and data packet dropouts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).

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