Outer synchronization between two complex dynamical networks with nonidentical coupling structures via time-varying delay feedback control

This paper is to design time-varying delay feedback controllers for outer synchronization between two complex dynamical networks with nonidentical coupling structures. By constructing the Lur´e-Postnikov Lyapunov functional, a new delay-dependent synchronization criterion is derived and formulated in the form of linear matrix inequalities (LMIs). Then, sufficient conditions on the existence of a time-varying delay feedback controller are obtained by using this newly-obtained synchronization criterion. The controller gains can be derived. A numerical example is given to illustrate the effectiveness of the synchronization criteria and the design method.