Global synchronization in Lur´e complex dynamical networks with delayed nodes and delayed coupling

This paper is concerned with the global synchronization in Lur´e complex dynamical networks. Compared with the existing complex dynamical networks with the time delay either in every node or in coupling part, this class of Lur´e complex dynamical networks not only have the time-delayed nodes, but also have the time-delayed coupling. These two classes of time delays are different from each other. By using LMI technique, synchronization criteria of this class of Lur´e complex dynamical networks are derived. These synchronization criteria are delay-dependent not only for the time delay in every node, but also for the time delay in the coupling part. A numerical example demonstrates the effectiveness of synchronization results.