On the Connections Between Various Stability Notions for Linear 2-D Discrete Models

In this article, we review different stability definitions that have been used in the literature concerning 2-D Roesser or Fornasini–Marchesini models: structural stability, asymptotic stability, and two different notions of exponential stability. We clarify the relations between all these definitio...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-12, Vol.68 (12), p.7919-7926
Main Authors: Bachelier, Olivier, Cluzeau, Thomas, Rigaud, Alexandre, Alvarez, Francisco José Silva, Yeganefar, Nader, Yeganefar, Nima
Format: Article
Language:English
Subjects:
Asymptotic properties
Automatic Control Engineering
Computer Science
Structural stability
Two dimensional models
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Summary:In this article, we review different stability definitions that have been used in the literature concerning 2-D Roesser or Fornasini–Marchesini models: structural stability, asymptotic stability, and two different notions of exponential stability. We clarify the relations between all these definitions for the linear case: the two notions of exponential stability and structural stability are all equivalent and they imply asymptotic stability.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3259976