Observer-Based Sliding Mode Control for a Class of Nonlinear Systems with Distributed Delays

This paper is concerned with the sliding mode observer design and observer-based controller design for a class of uncertain nonlinear distributed delay systems. According to the sliding mode control theory, first, a sufficient condition is proposed for robust asymptotic stability of the sliding mode dynamics. A sliding mode observer is designed, and at the same time, a sufficient condition is given for the existence of such an observer in terms of LMI. Based on estimated system state, a controller is synthesized by using the sliding mode control theory combining with the reaching law technology. This proposed control scheme guarantees the reachability of the sliding surfaces defined in both the state estimation space and the state estimation error space. Numerical example is given to illustrate the proposed design scheme.