This paper investigates the regularity, non-impulsiveness, stability and admissibility of the singular fractional-order systems with the fractional-order $\alpha \in (0,1)$ . Firstly, the structure, existence and uniqueness of the time domain solutions of singular fractional-order systems are analyzed based on the Kronecker equivalent standard form. The necessary and sufficient condition for the regularity of singular fractional-order systems is proposed on the basis of the above analysis. Secondly, the necessary and sufficient conditions of non-impulsiveness as well as stability are obtained based on the proposed time domain solutions of singular fractional-order systems, respectively. Thirdly, two novel sufficient and necessary conditions for the admissibility of singular fractional-order systems are derived including the non-strict linear matrix inequality form and the linear matrix inequality form with equality constraints. Finally, two numerical examples are given to show the effectiveness of the proposed results.

中文翻译：

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奇异分数阶系统的时域解分析和新的容许条件

本文研究了分数阶$\alpha\in (0,1)$的奇异分数阶系统的规律性、非冲动性、稳定性和可容许性。首先，基于Kronecker等效标准形式，分析了奇异分数阶系统时域解的结构、存在性和唯一性。在上述分析的基础上，提出奇异分数阶系统正则性的充要条件。其次，基于所提出的奇异分数阶系统的时域解，分别得到了非脉冲性和稳定性的充要条件。第三，推导出了奇异分数阶系统可接纳性的两个新的充要条件，包括非严格线性矩阵不等式和带等式约束的线性矩阵不等式。最后，给出了两个数值例子来证明所提出结果的有效性。