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Unimodular equivalence and similarity for linear systems

Vafiadis, D. & Karcanias, N. ORCID: 0000-0002-1889-6314 (2018). Unimodular equivalence and similarity for linear systems. International Journal of Control, 92(9), pp. 2091-2098. doi: 10.1080/00207179.2018.1427892


The problem of finding the mapping between unimoduar transformations relating two minimal matrix fraction descriptions (MFDs) of a transfer function, and the similarity transformations relating the respective minimal state-space representations is considered. It is shown that the problem is equivalent to finding the relation of MFDs of the input-state transfer functions of the two systems. This relation turns out to be an equivalence relation involving the unimodular and the similarity matrices relating the MFDs and the state-space systems, respectively. A canonical form for MFDs under this equivalence relation is obtained and it is shown that it leads to a canonical state-space representation, via a realisation procedure.

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Control on 15 January 2018, available online:
Publisher Keywords: Linear systems, unimodular transformations, similarity, matrix fraction description
Departments: School of Science & Technology > Engineering
SWORD Depositor:
Text - Accepted Version
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