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.