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Cluster synchronisation of Lur’e dynamical networks

Cluster synchronisation of Lur’e dynamical networks

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  • Author(s): L. Guo 1 ; X. Nian 1 ; Y. Zhao 2 ; Z. Duan 2
    • View affiliations
    • Affiliations: 1: School of Information Science and Engineering, Central South University, Changsha, People’s Republic of China
      2: State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing, People’s Republic of China
  • Source: Volume 6, Issue 16, 1 November 2012, p. 2499 – 2508
    DOI:  10.1049/iet-cta.2012.0467 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Published

This study investigates the cluster synchronisation problem of complex networks with each node being a Lur’e system. Some criteria for cluster synchronisation are presented by using a local linear control strategy. According to Lyapunov stability theory, sufficient conditions are first established to realise cluster synchronisation of the Lur’e dynamical networks. Then, a sufficient condition in the frequency domain is also formulated in the framework of the absolute stability theory. The notion of the cluster-synchronised region is introduced, and some conditions guaranteeing the cluster-synchronised region are derived. Furthermore, the cluster synchronisation in the Lur’e networks with time-varying delay is considered. Finally, some numerical examples illustrate the effectiveness of the theoretical results.

Inspec keywords: linear systems; stability; complex networks; nonlinear dynamical systems; delays; time-varying systems; synchronisation; Lyapunov methods

Other keywords: complex network; linear control strategy; cluster synchronisation problem; Lur'e dynamical network; Lyapunov stability theory; sufficient condition; time-varying delay

Subjects: Nonlinear control systems; Time-varying control systems; Stability in control theory

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