Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control

Abstract

In this proposed article, a framework is presented for the analysis of the problem of synchronization of Markovian jumping discrete-time complex dynamical networks (CDNs) with probabilistic interval time-varying delay in the dynamical node and in the network coupling. The networks are expressed in terms of Kronecker product technique. The delay in time is taken to be unexpected and the probability distribution is known a prior. The synchronization is achieved by introducing a non-fragile procedure. This controller is subject to randomly occurring perturbation and is assumed to belong to the Binomial sequence. A suitable Lyapunov–Krasovskii functional (LKF) with triple summation terms is considered. By utilizing the reciprocal convex combination approach and Finsler׳s Lemma, conditions for the synchronization of networks are established in terms of linear matrix inequalities (LMIs). The effectiveness of the results obtained theoretically are illustrated through two numerical examples.