Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control

In this paper, the synchronization problem of a complex dynamical network with coupling time-varying delays via delayed sampled-data controller is investigated. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the Extended Wirtinger Inequality. From a convex representation of the sector-restricted nonlinearity in system dynamics, the stability condition based on Lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.