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A class of weighted general complex dynamical networks with coupling delays is investigated. 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. 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 condition for delay-dependent asymptotical synchronization stability is derived in the form of linear matrix inequalities based on the Finsler's Lemma. It is also shown that the whole networks can be stabilized by controlling only a few nodes. A numerical example is given to illustrate the theoretical results.