In this paper, the problem of asynchronous switching control is investigated for switched linear systems based on the mode-dependent average dwell time(MDADT) method, meanwhile, the time delay constraints of model-dependent controllers are considered. In actual situations, owing to signal transmission, system detection, and the like, the switching of controllers is often lagged behind their corresponding subsystems. Therefore, the time interval in which one subsystem operates is divided into two parts: the matched and the mismatched. The controller of each subsystem is designed according to its model-dependent dwell time. Then, combined with the lag time of controllers, the appropriate dwell time strategy is derived based on Lyapunov stability conditions and system parameters, and the global exponential stability of the asynchronous switched systems is guaranteed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.