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Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols

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  • Xuan, Deli
  • Tang, Ze
  • Feng, Jianwen
  • Park, Ju H.

Abstract

This paper considers the globally and exponentially adaptive cluster synchronization for a kind of nonlinearly and nonidentically coupled Lur’e dynamical networks with an asymmetrical coupling matrix and multiple time-varying delays. With considering the cluster-tree topology structures of the networks, a novel delayed impulsive pinning control protocol is proposed, which only imposed on the Lur’e systems in current cluster which have directed paths with those Lur’e systems in the other clusters. In view of the Lyapunov stability theorem, mathematical induction method and the average impulsive interval, sufficient conditions that guarantee the achievement of the cluster synchronization are derived with different initial values. Furthermore, in accordance with the designed adaptive updating laws, suitable feedback control strengths are obtained, which largely save the control costs. Finally, the validity of the theoretical analysis and the control schemes are illustrated by means of a numerical experiment.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006913
    DOI: 10.1016/j.chaos.2021.111337
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    References listed on IDEAS

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    Cited by:

    1. 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).
    2. Zhou, Lili & Zhang, Yuhao & Tan, Fei & Huang, Mingzhe, 2023. "Adaptive secure synchronization of complex networks under mixed attacks via time-controllable technology," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Wang, Xuezhen & Zhang, Huasheng, 2023. "Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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