Exponential synchronization of complex dynamical networks with Markovian jump parameters and stochastic delays and its application to multi-agent systems (Q1933673)

One of the significant and interesting phenomena in complex dynamical networks is synchronization. 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 of the system, the stability condition based on Lyapunov's stability theory is obtained by using linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time-varying delay. The results show that the use of a discontinuous Lyapunov functional can get less conservatism than the use of a continuous Lyapunov functional. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.