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

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

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

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.

Keywords: Cluster synchronization; Lur’e networks; Nonlinear coupling; Adaptive pinning control; Impulsive control (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006913

DOI: 10.1016/j.chaos.2021.111337

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