Global Synchronization of Complex Lur´e Networks

This paper concerns the global synchronization problem of a class of complex dynamical networks with each node being a Lur´e system whose nonlinearity satisfying a slope condition. The synchronization problem is reformulated in the framework of the absolute stability theory. It is shown that the global synchronization of the network can be reduced to the test of a LMI, which in turn guarantees the absolute stability of the corresponding Lur´e system whose dimension is the same as that of a single node. A circle type criterion in frequency domain is further presented, in virtue of which the synchronization of the network can be checked graphically. It is demonstrated that the synchronizabiliby of the network can be characterized by the second largest eigenvalue of its coupling matrix. Finally, a network of Chua´s oscillators is provided as a simulation example to illustrate the effectiveness of the theoretical results.