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.
This paper investigates the leader-following consensus problem of multi-agent systems where the leader is static and the controlling effect of each follower depends on its own state. The control protocols are proposed for two cases: i) for network with switching topologies and undirected information flow; ii) for network with directed information flow and communication time-delays. With the aid of several tools from algebraic graph, matrix theory and stability theory, the sufficient conditions guaranteeing leader-following consensus are obtained by constructing appropriate Lyapunov functions. Simulations are presented to demonstrate the effectiveness of our theoretical results.
