Synchronization stability of complex dynamical networks with probabilistic time-varying delays

A kind of complex dynamical networks with time-varying coupling delays is proposed. By some transformation, the synchronization problem of the complex networks is transferred equally into the stochastic asymptotical stability problem of a group of uncorrelated delay functional differential equations. Different from the common assumptions on the delay in the existing references, the delay in this paper is assumed to be random and its probability distribution is known a prior. In terms of the probability distribution of the delays, a new type of system model with probability-distribution-dependent parameter matrices is proposed, the sufficient condition for delay-dependent asymptotical synchronization stability is derived in the form of linear matrix inequalities, the solvability of derived conditions depends on not only the size of the delay, but also the probability of the delay taking values in some intervals. At last, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.