Observer-based discrete-time sliding mode control with computational time delay: the linear case

The discrete-time sliding mode controllers reported in the past have always neglected the computational delay that is inherent in any digital implementation. An observer-based discrete-time sliding mode controller is suggested to explicitly account for this delay. The case for plants described by linear models is discussed. It is shown that the trajectories will be guaranteed to stay in the neighborhood of the sliding surface despite the presence of bounded uncertainties. A simple example is used to illustrate the proposed technique