This paper defines a fuzzy descriptor system by extending the ordinary Takagi-Sugeno (T-S) fuzzy model. Several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities (LMIs), We illustrate a motivative example of defining the fuzzy descriptor system instead of the ordinary TS fuzzy model, An LMI design approach is employed to find stable feedback gains and a common Lyapunov function. In addition, this paper presents a nonlinear model following control for the fuzzy descriptor system, A new parallel distributed compensation, the so-called "twin parallel distributed compensations" (TPDC), to realize the nonlinear model following control is proposed, The TPDC fuzzy controller mirrors the structures of the fuzzy descriptor systems that represent a nonlinear system and a nonlinear reference model. We present a design technique based on the TPDC. All the design conditions are represented in terms of LMIs, The proposed method is a unified approach to nonlinear model following control, It contains the regulation and servo control problems as special cases. Finally, design examples are illustrated to show the utility of the nonlinear model following control.
