Exponential synchronization of a complex dynamical network with piecewise-homogeneous Markovian jump structure and coupling delay

Abstract

In this paper, exponential synchronization problem is studied for a complex dynamical network (CDN) with a class of Markovian jump structure with coupling-time delay. The CDN under consideration has a piecewise-Markovian jump structure with piecewise-constant transition rates (TRs). First piecewise-homogeneous Markovian process is modeled by two Markov chains then, the synchronization problem of the CDN is inspected by constructing Lyapunov-Krasovskii function with Markov dependent matrices. Ultimately, the controller gain matrices for guaranteeing the synchronization problem in terms of linear matrix inequalities (LMIs) are derived. A CDN with a Chua circuit dynamic for each node is given as a numerical example to show the effectiveness of the theoretical results.