Stabilization of a class of Takagi-Sugeno fuzzy fractional order systems based on fuzzy controller switching

Abstract

In this paper, the stability of fuzzy fractional order systems (FOSs)is discussed. Firstly, a fuzzy model of FOSs with switching controllers is presented. Then, the stability criteria of fuzzy FOS with order 0 < a < 1 and 1 < a < 2, respectively, are given. The stability conditions are composed of bilinear matrix inequalities (BMIs) and can be converted to linear matrix inequalities (LMIs). Moreover, the stabilizing switching laws of the state-dependent form are designed. Finally, two examples are given to verify the effectiveness of the proposed results.