This paper investigates the output tracking control issue for discrete-time switched affine systems. To achieve effective tracking performance, a novel Lyapunov function is constructed, which incorporates both the tracking error dynamics and switching characteristics to establish comprehensive stability criteria. Sufficient conditions for stability are established using a switching Lyapunov function, which are expressed in the form of linear matrix inequalities. The proposed control strategy significantly enhances the dynamic response performance, ensuring the system state can track the target trajectory within a specified time. Finally, the effectiveness and feasibility of the method are verified through numerical examples.