Synchronization of weighted general complex dynamical networks with coupling delays

A weighted general complex dynamical networks with coupling delay is proposed, which is undirected and connected. By some transformation, the synchronization of the complex networks is transferred equally into the asymptotical stability problem of a group of uncorrelated delay functional differential equations. Control of such networks is investigated by applying local feedback injections to a fraction of network nodes for continuous time. Furthermore, the less conservative sufficient conditions for delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities based on the reformulation of the system and the technique of a discretization scheme of the delay. It is also shown that the whole networks can be stabilized by controlling only one node. Numerical examples are given to illustrate the effectiveness of the proposed approach.