Synchronization analysis of complex dynamical networks with delayed and non-delayed coupling based on pinning control

This paper investigates two kinds of synchronization between two linearly coupled complex networks with non-delayed and delayed coupling via the pinning control method, including inner and outer synchronization. Based on Lyapunov stability theory and the linear matrix inequality, some sufficient conditions for the synchronization are derived by adding linear feedback or adaptive feedback controllers to a part of the nodes, and feedback controllers are also designed. With proper conditions, two coupled complex networks can realize the synchronization, i.e. inner synchronization inside each network and outer synchronization between them simultaneously. Numerical examples are presented to verify the effectiveness and correctness of the synchronization criteria.