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Based on the variable structure system theory, we develop a nonlinear fuzzy observer-controller design method for a class of uncertain nonlinear systems that can be represented by a Takagi-Sugeno fuzzy model. We use a sliding mode observer and a sliding mode controller as the local state observer and the local controller. In terms of linear matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller. We also derive LMI conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha-stability or generalized H2/Hinfin performance constraints. We show that the observer and the controller can be independently designed, i.e., the separation property holds. Finally, we give simple LMI-based design algorithms, together with an example.