Abstract
This chapter considers the global and exponential cluster synchronization problems for a kind of nonlinearly and nonidentically coupled Lur’e dynamical networks with an asymmetrical coupling matrix. By considering the cluster-tree topology structures of the networks, a novel delayed impulsive pinning control protocol is proposed, which is only imposed on the Lur’e systems in current cluster that has directed paths with those Lur’e systems in the other clusters. Furthermore, to simulate more practical situations, the stabilizing effects of time delay in impulses are fully considered. In view of the Lyapunov stability theorem, mathematical induction method, and the average impulsive interval, sufficient conditions that ensure the realization of the cluster synchronization are derived with different initial values. Finally, the validity of the theoretical analysis and the control schemes are illustrated by means of a numerical experiment.
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