Equivalence transformations of rational matrices and applications

N. P. KARAMPETAKIS Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54006, Greece

A. C. PUGH Department of Mathematical Sciences, Loughborough University, LE, 11 3TU, U.K.

A. I. VARDULAKIS Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54006, Greece

Abstract

The known theories of transformations between polynomial matrices are extended to the case of rational matrices. Specifically, Ω-equivalence between rational matrices having possibly different dimensions is defined, and this has the property of preserving the zero structure of rational matrices in the region Ω ⊆ C ∪ {∞}Some implications of this new equivalence transformation for linear system theory are also provided.

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