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# Minimal pencil realizations of rational matrix functions with symmetries

Published:1998-06-01
Printed: Jun 1998
• Ilya Krupnik
• Peter Lancaster
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## Abstract

A theory of minimal realizations of rational matrix functions $W(\lambda)$ in the pencil'' form $W(\lambda)=C(\lambda A_1-A_2)^{-1}B$ is developed. In particular, properties of the pencil $\lambda A_1-A_2$ are discussed when $W(\lambda)$ is hermitian on the real line, and when $W(\lambda)$ is hermitian on the unit circle.
 MSC Classifications: 93Bxx - Controllability, observability, and system structure 15A23 - Factorization of matrices