In this paper, a novel technique to achieve robustness in sliding mode control for discrete-time systems by measuring only its output is presented. The proposed technique is based on the approximation of an arbitrary discrete-time function by using various of its previous steps. Using this approach, the system disturbance is approximated by a dynamical system and as result, the plant model is extended. Based on the extended model, a state observer is designed to estimate both the system state and the disturbance. Using the observer state, a discrete-time sliding mode controller is then designed to robustly stabilize the perturbed system. The simulation results show the effectiveness of the proposed technique.