Proportional plus derivative state feedback controller design for a class of fuzzy descriptor systems

Abstract

ABSTRACTThis study focuses on the proportional plus derivative state feedback (PDSF) control problem for continuous-time nonlinear descriptor systems described by Takagi–Sugeno fuzzy models with distinct fuzzy rules appearing in both sides of the considered system. Without using any additional transformations, some new conditions are developed by means of the free-weighting matrix technique and presented in terms of linear matrix inequalities to ensure that the resultant closed-loop system is normal and stable. Explicit expression of the desired PDSF controller is also given. Furthermore, the obtained result is extended to a class of uncertain nonlinear descriptor systems with norm-bounded perturbations. Finally, three examples are presented to show the effectiveness of the proposed method.