An effective criterion for a stable factorisation of strictly nonsingular 2x2 matrix functions. Utilisation of the ExactMPF package

TL;DR

This paper introduces a method for stable factorisation of strictly nonsingular 2x2 matrix functions using the ExactMPF package in Maple, providing a sufficient condition for stable factorisation based on the stability region of polynomial matrices.

Contribution

It presents a novel criterion for stable factorisation of nonsingular 2x2 matrix functions utilizing an exact factorisation tool within Maple, advancing the analysis of stability regions.

Findings

Proposes a sufficient condition for stable factorisation.

Utilises the ExactMPF package for exact polynomial matrix factorisation.

Analyzes the stability region of canonical factorisations.

Abstract

In this paper, we propose a method to factorise of arbitrary strictly nonsingular 2x2 matrix functions allowing for stable factorisation. For this purpose, we utilise the ExactMPF package working within the Maple environment previously developed by the authors and performing an exact factorisation of a nonsingular polynomial matrix function. A crucial point in the present analysis is the evaluation of a stability region of the canonical factorisation of the polynomial matrix functions. This, in turn, allows us to propose a sufficient condition for the given matrix function admitting stable factorisation.