Cluster synchronization for delayed Lur'e dynamical networks based on pinning control

In this paper, the problem on cluster synchronization is investigated for continuous/discrete-time Lur'e type dynamical networks by using pinning control strategy. Through combining Jensen inequality with reciprocal convex technique, some sufficient conditions are derived to ensure the cluster synchronization for the addressed networks if the designed linear feedback controller is employed to every cluster. Moreover, the problems of the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which can help reduce the computation complexity. Finally, three numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.