This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays.Using an appropriate Lyapunov-Krasovskii functional,some delay-dependent sufficient conditions and an adaptation law including the master-slave parameters are established for designing a delayed synchronization law in terms of linear matrix inequalities(LMIs).The time-varying controller guarantees the H∞ synchronization of the two coupled master and slave systems regardless of their initial states.Particularly,it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal.Two numerical examples are given to demonstrate the effectiveness of the method.