Observer-based sliding mode control for nonlinear state-delayed systems

An observer-based sliding mode control problem is studied for state-delayed systems with unmeasurable states and nonlinear uncertainties. The main advantage of the proposed scheme is that it eliminates the need for state variables to be fully accessible for its control. This is possible through the use of a sliding mode controller, which performs its control by employing state estimates obtained from the sliding mode observer. By means of linear matrix inequalities, a sufficient condition is then given to ensure the asymptotic stability of the overall closed-loop state-delayed system composed of the observer dynamics and the estimation error dynamics. Furthermore, it is shown that the proposed control scheme ensures the reachability of the sliding surfaces in both the state estimate space and the estimation error space.