An optimal integral sliding mode control algorithm for linear discrete-time systems with matched bounded disturbances is proposed. Under the premise that poles of the open-loop system locate inside or on the unit circle, the scheme can semi-globally regulate the system in the presence of input saturation. The scheme is an effective combination of low-gain feedback and integral sliding mode, for it can satisfy the input limit via low-gain feedback and improve the robustness of the system to disturbances owin...