Some necessary and sufficient conditions for low order intervalpolytopes to contain a Hurwitz polynomial

摘要

We establish some fundamental structure theorems which establishnecessary and sufficient conditions for low order (less than eight)interval polytopes to contain a Hurwitz polynomial. For instance, aninterval polytope of polynomials, generated by an interval polynomial ofdegree five, contains a Hurwitz polynomial if and only if an exposed twodimensional face of the polytope contains a Hurwitz polynomial. It turnsout that these conditions are not uniform, in the sense, that thesedepend on the degree of the interval polynomial generating the intervalpolytope