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Original Articles

Unimodular equivalence and similarity for linear systems

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Pages 2091-2098 | Received 19 Jul 2017, Accepted 10 Jan 2018, Published online: 30 Jan 2018
 

ABSTRACT

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.

Disclosure statement

No potential conflict of interest was reported by the authors.

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