On the connections between two classical notions of multidimensional system equivalence

Mohamed S. Boudellioua, Thomas Cluzeau*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)3046-3053
Number of pages8
JournalInternational Journal of Control
Volume94
Issue number11
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • algebraic analysis
  • equivalence
  • Linear systems theory
  • matrices of operators
  • multidimensional (nD) systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

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