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 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.