Output feedback stabilization of uncertain fuzzy systems using variable structure system approach

Based on the variable structure system theory, an output feedback fuzzy control design method is developed for a class of uncertain nonlinear systems that can be represented by a T–S (Takagi–Sugeno) fuzzy model. The uncertain fuzzy systems under consideration may have mismatched uncertainties in the state matrix. As the local controller a compensator-based sliding mode output feedback controller with a nonlinear discontinuous term is used. In terms of linear matrix inequalities (LMIs), a sufficient condition is derived for the existence of the fuzzy controller guaranteeing a stable sliding motion. It is shown that the compensator gain and the switching surface parameter matrix can be characterized in terms of the solution of the LMI existence condition. Finally, an LMI-based design algorithm and numerical design examples are given.