Design of Non-fragile Controller for Singular Fractional Order Takagi–Sugeno Fuzzy Systems

Abstract

This paper investigates the stabilization problem of a class of singular fractional order fuzzy systems with order $$0<\alpha <1$$ . Firstly, by the method of full rank decomposition of matrix, equality constraint of admissibility criterion in most existing literature is eliminated. Next, we present a stabilization criterion for singular fractional order Takagi–Sugeno (T–S) fuzzy systems by designing non-fragile state feedback controllers. Then, applying an equivalent form of original system in admissibility, the non-fragile output feedback controllers are designed to guarantee the closed-loop systems stable. And for fractional order $$1<\alpha <2$$ case, using similar designing approaches, strict linear matrix inequality (LMI) stabilization criteria based on non-fragile state and output feedback controller are obtained. Finally, two numerical simulation examples are given to illustrate the effectiveness of the proposed method.