An effective criterion for a stable factorisation of strictly non-singular 2 × 2 matrix functions: use of the ExactMPF package

Abstract

In this paper, we propose a method to factorise arbitrary strictly non-singular 2 × 2 matrix functions, allowing for stable factorisation. For this purpose, we use the E x a c t M P F package working within the Maple environment previously developed by the authors and perform an exact factorisation of a non-singular 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.