Synchronization and state estimation for stochastic complex networks with uncertain inner coupling

Abstract

This paper addresses the synchronization and state estimation problems for an array of coupled discrete-time stochastic complex networks (SCNs) with uncertain inner couplings in which time-varying delay is considered both in the network couplings and dynamical nodes. In particular, the uncertainties encountering in coupling terms are characterized by using the interval matrix approach. By constructing a suitable Lyapunov–Krasovskii functional and utilizing Kronecker product properties, a new set of sufficient conditions is established in terms of linear matrix inequalities to guarantee the synchronization of the addressed SCNs with a prescribed mixed H∞ and passivity performance index. Moreover, the state estimation problem is then studied for the same SCNs with uncertain inner coupling strength and subsequently, the estimator is designed. More precisely, Schur complement, discrete-time Jensen’s inequality together with reciprocally convex combination approach are used to simplify the derivations in the main results. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed synchronization and state estimation results.