Fiedler Linearizations of Rectangular Rational Matrix Functions

TL;DR

This paper extends Fiedler linearizations, traditionally used for square matrices, to rectangular rational matrix functions, facilitating eigenvalue computations for systems like Rosenbrock functions in control theory.

Contribution

It generalizes Fiedler linearizations from square to rectangular rational matrix functions, broadening their applicability in system analysis.

Findings

Extended Fiedler linearizations to rectangular functions.

Applied to Rosenbrock functions in system theory.

Enhances eigenvalue computation methods for non-square systems.

Abstract

Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler linearizations, which are generalizations of the classical companion forms. In this paper the concept of Fiedler linearization is extended from square regular to rectangular rational matrix valued functions. The approach is applied to Rosenbrock functions arising in mathematical system theory.