Passivity-based synchronization of Markovian jump complex dynamical networks with time-varying delays, parameter uncertainties, reaction–diffusion terms, and sampled-data control

Abstract

The problem of passivity analysis of reaction–diffusion complex dynamical networks with time-varying delays and Markovian jumping parameters is considered in this article. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. Specially, the time varying delays are taken into consideration to describe the sample-data control of the system. 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 passivity-based synchronization of complex dynamical networks even in the case of uncertainty and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and reciprocal convex techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is passive. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results.