A necessary and sufficient condition of asymptotic stability for a class of Fornasini-Marchesini models

被引：0

作者：

Bachelier, Olivier ^{[1
]}

Cluzeau, Thomas ^{[2
]}

Rigaud, Alexandre ^{[1
]}

Silva Alvarez, Francisco Jose ^{[2
]}

Yeganefar, Nima ^{[1
]}

机构：

[1] Univ Poitiers, LIAS ENSIP, Batiment B25,2 Pierre Brousse,TSA 41105, F-86073 Poitiers, France

[2] Univ Limoges, XLIM, UMR CNRS 7252, 123 Ave Albert Thomas, F-87060 Limoges, France

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 658卷

关键词：

Linear systems; Multidimensional systems; 2D discrete systems; Fornasini-Marchesini models; Asymptotic stability; DISCRETE-SYSTEMS; STABILIZATION;

D O I：

10.1016/j.laa.2022.10.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the asymptotic stability of a particular class of linear2D discrete Fornasini-Marchesini models. The solutions of the model can be expressed in terms of doubly indexed sequences in a simple way only when the matrices describing the model commute. In this situation, we are able to analyse directly the limit of all the trajectories. By doing so, we propose the first necessary and sufficient condition for asymptotic stability of Fornasini-Marchesini matrix models. This condition is not computationally challenging as it is ultimately based on the eigenvalues of the matrices describing the model. We support our result with numerical simulations. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：206 / 232

页数：27

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