Pinning cluster synchronization of delay-coupled Lur’e dynamical networks in a convex domain

This paper devotes to investigating the cluster synchronization of coupled complex dynamical networks consisted of Lur’e systems with time-varying delay. By considering the topology structure of the complex network, an effective pinning controller is designed which not only synchronize all Lur’e sys...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-07, Vol.89 (1), p.623-638
Main Authors: Park, Ju H., Tang, Ze, Feng, Jianwen
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Clusters
Computer simulation
Control
Control systems design
Controllers
Delay
Dynamical Systems
Engineering
Mathematical models
Mechanical Engineering
Networks
Original Paper
Pinning
Stability criteria
Synchronism
Topology
Vibration
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Summary:This paper devotes to investigating the cluster synchronization of coupled complex dynamical networks consisted of Lur’e systems with time-varying delay. By considering the topology structure of the complex network, an effective pinning controller is designed which not only synchronize all Lur’e systems in the same cluster, but also decrease the influence among different clusters. Firstly, based on delay interval dividing methods, expended Jensen’s inequality and Jacobian methods, sufficient conditions for local cluster synchronization of the Lur’e dynamical networks are derived by applying the specially designed pinning controller. Secondly, the convex combination theorem, S-procedure and the definition of delay rate are jointly applied in order to obtain the delay-dependent stability criteria which guarantee the global cluster synchronization of the Lur’e networks under the pinning control strategy. And finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3476-3