Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction–diffusion terms via sampled-data control

Abstract

This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.