Cluster synchronization in networks of partial-state coupled linear systems via pinning control technique*

This paper investigates the cluster synchronization for network of linear systems under general topology via pinning control technique. It is shown that an appropriate feedback controller can be designed to achieve the given cluster synchronization pattern if the induced network topology of each cluster has a directed spanning tree and further compared to the couplings among different clusters, the couplings within the each cluster are sufficiently strong. Both the lower bounds for such strengths of couplings and the cluster synchronization rate are specified as well. Finally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings.