Robust Discrete-Time Sliding Mode Control with Arbitrarily Small Boundary Layer

The robust discrete-time sliding mode control problem is addressed. A novel approach to estimate the matched disturbance is presented. This approach is based on the approximation of a discrete-time function actual value by using various previous steps of itself. The matched disturbance previous step is calculated from the system model and then, using the mentioned approach, its actual value is estimated with an error of exponential order w.r.t. the sampling time and the used number of previous steps. Simulations show the effectiveness of the proposed approach to estimate a discrete time function and to robustly stabilize a dynamic system.