Cluster synchronisation of Lur´e dynamical networks

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.