Fuzzy descriptor systems and nonlinear model following control

This paper defines a fuzzy descriptor system by extending the ordinary Taka gi-Sugeno (T-S) fuzzy model. Several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matr ix inequalities (LMIs), We illustrate a motivative example of defining the fuzzy descriptor system instead of the ordinary TS fuzzy model, An LMI desi gn approach is employed to find stable feedback gains and a common Lyapunov function. In addition, this paper presents a nonlinear model following con trol for the fuzzy descriptor system, A new parallel distributed compensati on, the so-called "twin parallel distributed compensations" (TPDC), to real ize the nonlinear model following control is proposed, The TPDC fuzzy contr oller mirrors the structures of the fuzzy descriptor systems that represent a nonlinear system and a nonlinear reference model. We present a design te chnique based on the TPDC. All the design conditions are represented in ter ms of LMIs, The proposed method is a unified approach to nonlinear model fo llowing control, It contains the regulation and servo control problems as s pecial cases. Finally, design examples are illustrated to show the utility of the nonlinear model following control.