Adaptive sliding mode observer-controller design for nonlinear systems: a fuzzy approach

In this paper, the problems of observer-based sliding mode control for a class of nonlinear system are investigated via Takagi-Sugeno (T-S) fuzzy approach. By using the T-S model as the design model, an adaptive sliding mode observer is first constructed to estimate the states of the original nonlinear system without knowing any information of the actuator fault. And then, a sliding mode surface in the state-estimation space is proposed and a new sliding mode controller which can force the motion of closed-loop system onto the surface is designed. Besides, the sufficient conditions of the existence of the observer and controller are provided in terms of linear matrix inequalities (LMIs). Finally, the ball and beam system is used as an example to verify the validity of the proposed method.