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

In this paper, we study the asymptotic stability of a particular class of linear 2D 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 ab...

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Veröffentlicht in:	Linear algebra and its applications 2023-02, Vol.658, p.206-232
Hauptverfasser:	Bachelier, Olivier, Cluzeau, Thomas, Rigaud, Alexandre, Silva Àlvarez, Francisco José, Yeganefar, Nima
Format:	Artikel
Sprache:	eng
Schlagworte:	2D discrete systems Asymptotic stability Automatic Control Engineering Computer Science Fornasini-Marchesini models Linear systems Multidimensional systems
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creator	Bachelier, Olivier Cluzeau, Thomas Rigaud, Alexandre Silva Àlvarez, Francisco José Yeganefar, Nima
description	In this paper, we study the asymptotic stability of a particular class of linear 2D 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.
doi_str_mv	10.1016/j.laa.2022.10.026
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subjects	2D discrete systems Asymptotic stability Automatic Control Engineering Computer Science Fornasini-Marchesini models Linear systems Multidimensional systems
title	A necessary and sufficient condition of asymptotic stability for a class of Fornasini-Marchesini models
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