This paper investigates the stabilizing state feedback controller design problem for a class of discrete-time systems with mismatched disturbances based on generalized extended state observers. In the traditional active disturbance rejection controller, the extended state observer is designed for systems with matched disturbances and integral series structure. However, in many practical applications, the disturbances are usually mismatched, for example, in discrete-time systems with sampling chattering. Therefore, a design method is presented for generalized extended state observers and corresponding stabilizing state feedback controllers for a class of discrete-time systems with mismatched disturbances. A simulation example of the speed regulator for the permanent magnetic synchronous motor is presented to illustrate the effectiveness of the proposed observer and controller.