Robust H_∞ cluster synchronization analysis of Lurie dynamical networks

The cluster synchronization problem of complex dynamical networks with each node being a Lurie system with external disturbances and time-varying delay is investigated in this paper. Some criteria for cluster synchronization with desired H_∞ performance are presented by using a local linear control scheme. Firstly, sufficient conditions are established to realize cluster synchronization of the Lurie dynamical networks without time delay. Then, the notion of the cluster synchronized region is introduced, and some conditions guaranteeing the cluster synchronized region and unbounded cluster synchronized region are derived. Furthermore, the cluster synchronization and cluster synchronized region in the Lurie dynamical networks with time-varying delay are considered. Numerical examples are finally provided to verify and illustrate the theoretical results.