On estimating regions of stability of the estimation error of sliding mode observers for uncertain systems

Two classes of full-order sliding mode observers for uncertain dynamical systems are analyzed. The first class has its roots in the sliding mode equivalent-control method, while the second class is based on the second method of Lyapunov. The observers are analyzed using differential inequalities that appear in the analysis of a class of sliding mode controllers. Using the differential inequalities, regions of stability of the estimation error are determined. In addition, uniform ultimate boundedness of the estimation error is proven for the equivalent-control based class of sliding mode observers for uncertain dynamical systems