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Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays

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  • Yang, Te
  • Wang, Zhen
  • Huang, Xia
  • Xia, Jianwei

Abstract

This paper studies the mean square exponential synchronization control of the Markovian jump chaotic Lur'e systems (MJCLSs) with multiple time delays under aperiodic sampling. Firstly, by introducing the mode-dependent single/double integral terms and considering the system state at the sampling instant, a new mode-dependent Lyapunov functional based on the looped-functional is constructed. On the basis of the constructed functional and by estimating the expectation of the solution of MJCLSs with multiple time delays, an exponential synchronization criterion in the mean square sense is presented. Then, based on the obtained stability conditions, a design method for aperiodic sampled-data controller (ASDC) to ensure the exponential synchronization is proposed. Finally, the effectiveness of the developed method is demonstrated by the Chua's circuit model and a neural network model. Compared with the existing literature, an admissible larger upper bound of sampling period can be obtained.

Suggested Citation

  • Yang, Te & Wang, Zhen & Huang, Xia & Xia, Jianwei, 2022. "Sampled-data exponential synchronization of Markovian jump chaotic Lur'e systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004623
    DOI: 10.1016/j.chaos.2022.112252
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    References listed on IDEAS

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    1. Jun Huang & Peng Wang & Zhengzhi Han & Xiushan Cai, 2013. "Observer design for the Lur'e differential inclusion system with Markovian jumping parameters," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(12), pages 2338-2348.
    2. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Hu, Rongchun & Zhang, Dongxu & Gu, Xudong, 2022. "Reliability analysis of a class of stochastically excited nonlinear Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Yu, Tianhu & Cao, Dengqing & Yang, Yang & Liu, Shengqiang & Huang, Wenhu, 2016. "Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 92-101.
    5. Cao, Jinde & Li, H.X. & Ho, Daniel W.C., 2005. "Synchronization criteria of Lur’e systems with time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1285-1298.
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    Cited by:

    1. Guo, Beibei & Xiao, Yu, 2023. "Intermittent synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump and its application of Chua’s circuits," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Feng, Zhiguang & Feng, Bo & Zhang, Naifu, 2023. "Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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