Stability analysis and stabilisation of continuous-discrete fractional-order 2D Fornasini-Marchesini first model

被引：5

作者：

Zhang, Jia-Rui ^{[1
,2
,3
]}

Lu, Jun-Guo ^{[1
,2
,3
]}

Zhu, Zhen ^{[1
,2
,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] Shanghai Engn Res Ctr Intelligent Control & Manag, Shanghai 200240, Peoples R China

来源：

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE | 2023年 / 54卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Continuous-discrete two-dimensional Fornasini-Marchesini first model; structural stability; Generalized-Kalman-Yakubovich-Popov Lemma; fractional order; stabilisation; linear matrix inequality; SYSTEMS; INEQUALITY; MATRIX; DESIGN;

D O I：

10.1080/00207721.2022.2122901

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 paper focuses on the structural stability and stabilisation of the continuous-discrete fractional-order two-dimensional Fornasini-Marchesini first model. The sufficient and necessary stability conditions are given in polynomial form at first. Secondly, to make the problem solvable, based on the property of Kronecker product and the Generalized-Kalman-Yakubovich-Popov Lemma, the new sufficient and necessary stability conditions are established in the form of linear matrix inequalities. Thirdly, with the help of the Projection Lemma, the stabilisation conditions are obtained after introducing a state feedback controller, which can be solved with an iterative linear matrix inequality algorithm. In the end, the effectiveness of the proposed results is verified by two numerical examples.

引用

页码：333 / 344

页数：12

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