Robust non-fragile proportional plus derivative state feedback control for a class of uncertain Takagi–Sugeno fuzzy singular systems

Abstract

This paper proposes a novel robust non-fragile proportional plus derivative state feedback (PDSF) control scheme for a class of uncertain nonlinear singular systems. The Takagi–Sugeno (T–S) fuzzy model is employed to represent the nonlinear singular system with parameter uncertainties appearing not only in distinct state matrices, but also in distinct derivative matrices. By using the free-weighting matrix technique, some sufficient conditions, which guarantee the resulting closed-loop system to be normal and stable (NS), are presented. With these conditions, the problems of non-fragile PDSF controllers design with additive and multiplicative uncertainties are respectively solved in terms of linear matrix inequalities (LMIs), which can be conveniently solved via the convex optimization technique. Finally, two examples are provided to illustrate the validity of the presented results.