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Ideally, switching between subsystems and controllers occurs synchronously. In other words, whenever a subsystem requires switching, its corresponding sub-controller will be promptly activated. However, in reality, due to network delays, system detection, etc., the activation of candidate controllers frequently lags, which causes issues with asynchronous switching between controllers and subsystems. This asynchronous switching problem may affect system performance and even make the system unstable because the state between the subsystem and the controller may be inconsistent, resulting in the controller not being able to control the subsystem correctly. To keep the system stable while using asynchronous switching, this work suggests an asynchronous control technique for a class of discrete linear switching systems with time delay based on the mode-dependent average dwell time (MDADT). First, we construct a state feedback controller and establish a closed-loop system. In the asynchronous and synchronous intervals of subsystems and controllers, different Lyapunov functions are selected, and sufficient conditions for exponential stability and the H ∞ performance of the closed-loop system under asynchronous switching are obtained. In addition, using the MDADT switching strategy, the relevant parameters of each subsystem are designed and the corresponding state–feedback controller gain matrix can be obtained. Finally, a switching system with three subsystems is shown. The approach is confirmed by simulating it using the average dwell time (ADT) switching strategy and the MDADT switching strategy separately. [ABSTRACT FROM AUTHOR]