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

被引：20
|
作者：
Zhang, Qing-Hao [1 ,2 ]
Lu, Jun-Guo [1 ,2 ]
Ma, Ying-Dong [1 ,2 ]
Chen, Yang-Quan [3 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Automat, Shanghai 200240, Peoples R China
[2] Minist Educ China, Key Lab Syst Control & Informat Proc, Shanghai 200240, Peoples R China
[3] Univ Calif Merced, Sch Engn, Mechatron Embedded Syst & Automat MESA Lab, Merced, CA 95343 USA
来源：
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS | 2021年 / 68卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Singular fractional-order system; the time domain solution; regularity; non-impulsiveness; stability; admissibility;
D O I：
10.1109/TCSI.2020.3036412
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
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.
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页码：842 / 855
页数：14
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