Pinning Cluster Synchronization for Delayed Dynamical Networks via Kronecker Product

Abstract

In this paper, the cluster synchronization is investigated for a class of dynamical networks composed of N delayed Lur’e systems by using pinning control strategy. Through combining the Kronecker product with reciprocal convex technique, some sufficient conditions are derived to ensure the cluster synchronization for the addressed networks such that the designed linear feedback controller can be employed to every cluster. Especially, the inner coupling matrices are not restricted to be diagonal and the problems of the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which extend the application area and reduce the computational complexity. Finally, three numerical examples are provided to demonstrate the effectiveness of the derived results.