Discrete-time adaptive sliding mode control of a linear system in state-space form

A discrete-time adaptive sliding mode controller for linear systems represented by the state space is presented. The controller is developed using the delta operator, which is better for approximating continuous-time systems than the shift operator. The use of the delta model allows the selection of the sliding surface to be similar to that for the continuous-time case. It is shown that the adaptive control algorithm leads to a stable closed-loop system. Simulation results are presented to illustrate the features of the proposed control scheme.