Observer-based PI sliding mode controller design of a class of switched systems

This paper studies the observer-based proportional-integral (PI) sliding mode control problem for a class of switched systems. Our goal is to stabilize the switched system by selecting a suitable Lyapunov function and giving a sufficient condition through the sliding mode controlled PI observer when the system states are inaccessible. The main results are presented and proved in means of linear matrix inequality technique. In order to approximate the correlation equation with satisfactory accuracy, we describe the relevant design problem as a semidefinite programming by regular convex optimization.