Time Domain Solution Analysis and Novel Admissibility Conditions of Singular Fractional-Order Systems

This paper investigates the regularity, nonimpulsiveness, stability and admissibility of the singular fractional-order systems with the fractional-order alpha is an element of (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.

Automated summary

This paper investigates the regularity, nonimpulsiveness, stability and admissibility of singular fractional-order systems with a fractional-order alpha in the range of (0, 1). Necessary and sufficient conditions for regularity, non-impulsiveness, stability, and admissibility are proposed based on the analysis of time domain solutions. Novel conditions for admissibility are derived, including non-strict linear matrix inequality form and linear matrix inequality form with equality constraints.