ON SYNCHRONIZATION OF DISCRETE-TIME MARKOVIAN JUMPING STOCHASTIC COMPLEX NETWORKS WITH MODE-DEPENDENT MIXED TIME-DELAYS

Abstract

In this paper, the synchronization problem is investigated for a new class of discrete-time complex networks. Such complex networks involve the Markovian jumping parameters, mode-dependent discrete and distributed time-delays, constant and delayed couplings, as well as multiple stochastic disturbances. The stochastic disturbances influence the constant coupling term, the delayed coupling term, as well as the overall network dynamics, which could better describe the dynamical behavior of a coupled complex network presented within a noisy environment. With help from the Lyapunov functional method and the properties of Kronecker product, we employ the stochastic analysis techniques to derive several delay-dependent sufficient conditions under which the coupled complex network is asymptotically synchronized in the mean square. The criteria obtained in this paper are in the form of LMIs whose solution can be easily calculated using the standard numerical software. It is shown that our main results can cover many existing ones reported in the literature. A numerical example is presented to illustrate the usefulness of our results.