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.

本文重点研究分数阶模糊奇异摄动系统通过阶数为 0 < α 的状态和静态输出反馈控制的稳定条件< 1，分别。首先，通过等效变换，将分数阶奇异摄动系统转化为分数阶奇异系统。其次，提出了状态反馈控制下的三个稳定条件。然后，在引入中间变量的基础上，得到了保证分数阶Takagi-Sugeno模糊奇异摄动系统稳定的严格线性矩阵不等式的静态输出反馈控制条件。并且提出的条件可以克服现有工作中的一些缺点。最后，提供了两个例子来说明本研究结果的有效性。