Observer with multiple sliding modes for a class of nonlinear uncertain systems

Sliding mode observer design for a class of nonlinear uncertain systems is systematically developed in this paper. The observer is designed under less conservative conditions than existing sliding mode observers that are based on equivalent control concept. A methodology to select suitable transformation is formulated, and it divides the original system into three interconnected subsystems. Multiple sliding modes are then introduced to compensate for multiple disturbance terms in the subsystems by appending them to constant gain observer. The conditions for asymptotic stability of estimation error dynamics have been derived based on Lipschitz assumptions for nonlinear functions by standard Lyapunov analysis. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.