Stability analysis of polynomials with an approach of differential topology

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