Adaptive synchronization of asymmetric coupled networks with multiple coupling delays

The synchronization problem of asymmetric networks with multiple coupled delays is investigated in this paper. By using Lyapunov stability theory and Lasalle's invariance principle, several synchronization criteria are deduced for both asymmetric networks with and without norm uncertainties. Furthermore, the synchronization problem of a special complex network with each node being a Lurie system is studied. The main results show that the states of all nodes of networks globally asymptotically synchronize to a desired synchronization state by designing suitable adaptive controllers, and these controllers have strong robustness against the uncertain coupling matrixes. Finally, several illustrative examples with numerical simulations are given to show the feasibility and efficiency of theoretical results.