Synchronization for discrete-time complex dynamical networks with time-varying delays

A class 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 asymptotical stability problem of a group of uncorrelated delay functional differential equations. The delays considered in this paper are assumed to vary in an interval, where the lower and upper bounds are known. The free weighting matrices are employed to deal with cross product items, and the convexity of the matrix function is fully utilized in our proof, the sufficient condition for delay-dependent asymptotical synchronization stability is derived in the form of linear matrix inequalities. Numerical examples are given to illustrate the theoretical results.