Stable polynomial curves and some properties with application in control

The aim of this work is to give a Hurwitz path (which is a family of polynomials) joining any two arbitrary stable polynomials in the set of monic Hurwitz polynomials with positive coefficients and fixed degree n, \(\mathcal {H}_{n}^{+}\). This and the homotopy of paths allow to prove the existence of a dense trajectory in \(\mathcal {H}_{n}^{+}\). It implies, by the Mobius transform and Viete’s map, that we can find a connecting-path in the set of the Schur polynomials, \(\mathcal {S}_{n}\). Due to the form of the stable connecting-paths, a feedback control is designed whose structure can be used to stabilize continuous or discrete systems.