In this thesis, we extend the design of integral-type sliding mode control from a continuous-time nonlinear uncertain system to a class of discrete-time nonlinear uncertain system, in which the uncertainty satisfies the matching condition. The selected sliding surface has two main features. First, the initial states locate on the sliding surface from beginning, so that the robustness of the system can be improved. Second, when the states remain on the sliding surface, the uncertain system behaves the same as the nominal system has, therefore, the engineer may perform their optimal design with respect to the nominal system according to requirements. Furthermore, the integral-type sliding surface is also combined with the quasi-sliding mode controller, to find out the quasi-sliding mode band (QSMB).