Stability analysis of polynomials with an approach of differential topology

Abstract

SummaryIn this paper, we study the Hurwitz stability of polynomials. By considering that a degree Hurwitz polynomial has its corresponding Markov parameters, we define the set in Section 3, we also define . Based on properties of the Hankel matrices and the stability test, as well as by using ideas of differential topology, we show that is a fiber bundle with a base. This result allows us to obtain an interesting application: Given a Hurwitz polynomial, we can generate two families of positive definite Hankel matrices.