TY - JOUR
T1 - On the connections between two classical notions of multidimensional system equivalence
AU - Boudellioua, Mohamed S.
AU - Cluzeau, Thomas
N1 - Funding Information:
The second author would like to thank Olivier Bachelier and Alban Quadrat for helpful discussions about the subject of the present article. We also thank the anonymous referees of the paper for their remarks which allow to improve the clarity of the paper.
Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - In this paper, we study the connections between two classical notions of equivalence used in the literature of linear multidimensional (nD) systems. On one hand, we have the notion of zero coprime system equivalence which has been proved to be well suited for the preservation of input–output properties. On the other hand, we have the notion of equivalence induced by the algebraic analysis approach to linear systems theory which preserves algebraic properties of the associated module. We first prove that a zero coprime system equivalence yields an equivalence in the sense of algebraic analysis. Conversely, we show that, under some conditions, an equivalence in the sense of algebraic analysis provides a zero coprime system equivalence. In both cases, the results are completely explicit.
AB - In this paper, we study the connections between two classical notions of equivalence used in the literature of linear multidimensional (nD) systems. On one hand, we have the notion of zero coprime system equivalence which has been proved to be well suited for the preservation of input–output properties. On the other hand, we have the notion of equivalence induced by the algebraic analysis approach to linear systems theory which preserves algebraic properties of the associated module. We first prove that a zero coprime system equivalence yields an equivalence in the sense of algebraic analysis. Conversely, we show that, under some conditions, an equivalence in the sense of algebraic analysis provides a zero coprime system equivalence. In both cases, the results are completely explicit.
KW - algebraic analysis
KW - equivalence
KW - Linear systems theory
KW - matrices of operators
KW - multidimensional (nD) systems
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U2 - 10.1080/00207179.2020.1749939
DO - 10.1080/00207179.2020.1749939
M3 - Article
AN - SCOPUS:85083553673
SN - 0020-7179
VL - 94
SP - 3046
EP - 3053
JO - International Journal of Control
JF - International Journal of Control
IS - 11
ER -