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This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory.First,by a common unitary matrix,the problem of synchronization is transformed in to the stability analysis of some linear switched delay systems.Then,when all subnetworks arc synchronizable.a delayaependent suffcient condition is given in terms of linear matrix inequalities(LMIs)which guarantees the solvability of the syncttronlzation problem under an average dwell time scheme.We extend this result to the case that not all subnetworks are synchronizable.It iS shown that in addition to average dwell time.if the ratio of the toml activation time of synchronizable and non-synchronizable subnetworks sarisfy an extra condition,then the problem is also solvable.Two numerical examples of delayed dynamical networks with switching topology are given,which demonstrate the effectiveness of obtained results.