Distributed adaptive pinning control for cluster synchronization of nonlinearly coupled Lur'e networks

This paper is devoted to the cluster synchronization issue of nonlinearly coupled Lur'e networks under the distributed adaptive pinning control strategy. The time-varying delayed networks consisted of identical and nonidentical Lur'e systems are discussed respectively by applying the edge-based pinning control scheme. In each cluster, the edges belonging to the spanning tree are pinned. In view of the nonlinearly couplings of the networks, for the first time, an efficient distributed nonlinearly adaptive update law based on the local information of the dynamical behaviors of node is proposed. Sufficient criteria for the achievement of cluster synchronization are derived based on S-procedure, Kronecker product and Lyapunov stability theory. Additionally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical results.