Abstract
This paper investigates the regularity, nonimpulsiveness, stability and admissibility of the singular fractional-order systems with the fractional-order α ∈ (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.
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