Strictly Stable Hurwitz Polynomials and their Determinantal Representations

TL;DR

This paper develops certifying determinantal representations for multivariable polynomials with strictly stable factors using Cayley transforms and Hermitian Positivstellensatz, advancing the understanding of stability and determinantal representations.

Contribution

It introduces new certifying determinantal representation results for strictly stable multivariable polynomials, utilizing advanced algebraic and transform techniques.

Findings

Established determinantal representations for stable polynomials

Connected stability conditions with Hermitian Positivstellensatz

Provided methods for certifying polynomial stability

Abstract

We establish various certifying determinantal representation results for a polynomial that contains as a factor a prescribed multivariable polynomials that is strictly stable on a tube domain. The proofs use a Cayley transform in combination with the Matrix-valued Hermitian Positivstellensatz developed in ArXiv:1501.05527.