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

• Published in: IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2021-02, Vol.68 (2), p.842-855
• Main Authors: Zhang, Qing-Hao, Lu, Jun-Guo, Ma, Ying-Dong, Chen, Yang-Quan
• Format: Article
• Language: English
• Subjects: admissibility; Asymptotic stability; Circuit stability; Linear matrix inequalities; non-impulsiveness; Numerical stability; Regularity; Singular fractional-order system; Stability; Stability criteria; Symmetric matrices; the~time domain solution; Time domain analysis; Uncertainty
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2020.3036412

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.