Positive real lemmas for singular fractional-order systems: the 0 < α < 1 case

被引：9
作者：
Zhang, Qing-Hao [1 ,2 ]
Lu, Jun-Guo [1 ,2 ]
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
来源：
IET CONTROL THEORY AND APPLICATIONS | 2020年 / 14卷 / 18期
基金：
中国国家自然科学基金;
关键词：
linear systems; linear matrix inequalities; control system synthesis; stability; singular fractional-order systems; positive real lemmas; singular fractional-order linear time-invariant systems; fractional order alpha; strictly positive realness; positive real controller synthesis problems; corresponding positive real controllers; STABILIZATION; STABILITY;
D O I：
10.1049/iet-cta.2020.0527
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This study investigates the positive real lemmas for singular fractional-order linear time-invariant systems with the fractional order alpha is an element of (0, 1). Firstly, a novel condition for the stability and extended strictly positive realness of fractional-order systems is derived in terms of linear matrix inequalities. Secondly, a novel condition for the admissibility and extended strictly positive realness of singular fractional-order systems is obtained with two complex variables. Then, another novel condition for the admissibility and extended strictly positive realness of singular fractional-order systems is established with only one complex variable. Thirdly, the positive real controller synthesis problems are analysed and the corresponding positive real controllers are designed based on the positive real lemmas. Finally, four numerical examples are provided to show the effectiveness of the proposed results in this study.
引用
收藏
页码：2805 / 2813
页数：9
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