Cluster Synchronization of Nonlinearly Coupled Lur'e Networks with Non-identical Nodes under Adaptive Pinning Control

The problem of global adaptive cluster synchronization in complex dynamic networks formed by nonlinear Lur'e systems with asymmetrical and non-identical couplings is investigated in this paper. Only Lur'e systems in the current cluster with direct connectivity to other clusters are controlled by an efficient pinning feedback controller. The Lyapunov stability theorem, the S-procedure, the emphS-procedure, and other mathematical analysis are used to derive certain conditions that ensure the cluster synchronization's realization. Furthermore, the adaptive update laws given are employed to acquire the optimal feedback control gains. Ultimately, one numerical simulation is provided to verify the obtained results.