Output feedback control of fractional order Takagi–Sugeno fuzzy singularly perturbed systems

Abstract

This article focuses on the stabilization conditions of fractional order fuzzy singularly perturbed systems via state and static output feedback control with order 0 < α < 1, respectively. First, by an equivalent transformation, fractional order singularly perturbed systems are transformed into fractional order singular systems. Second, three stabilizing conditions under state feedback control are proposed. Then, based on the introduction of intermediate variables, static output feedback control condition in terms of strict linear matrix inequalities which guarantee the fractional order Takagi–Sugeno fuzzy singularly perturbed system to be stable is obtained. And the proposed conditions can overcome some drawbacks in the existing work. Finally, two examples are provided to show the effectiveness of the results in this study.