Sliding mode control for a class of nonlinear systems with distributed delay

The design problems of sliding mode observer and the observer-based controller are addressed for a class of uncertain nonlinear systems with distributed delays. According to the sliding mode control theory, we propose a sufficient condition of robust asymptotic stability for the sliding mode dynamics. A sliding mode observer is designed, and the sufficient condition is given for the existence of such an observer in terms of linear matrix inequality (LMI). Based on the observed states, a controller is synthesized by using the sliding mode control theory and the reaching law technique. The proposed control scheme guarantees the reachability of the sliding surfaces defined in both the observed state space and the observed state-error space.