Constructing convex directions for stable polynomials

The constructions of convex directions based on phase-derivative interpretations were obtained for Hurwitz-stable polynomials. The phase-derivative conditions were based on the sensitivity of root-locus associated with the even and odd parts of a polynomial. The phase-growth condition directly established anti-Hurwitz polynomials, polynomials of degree one, even polynomials and odd polynomials for the entire set of Hurwitz polynomials.