Convex compact family of polynomials and its stability

Abstract. Let \(P\) be a set of real polynomials of degree \(n\). Set \(P\) can be identified with some subset \(P\) of \(\mathbb{R}^n\) consists of vectors of coefficients of \(P\). If \(P\) is a polytope, then to ascertain whether the entire family of polynomials \(P\) is stable or not, it suffices to examine the stability of the one-dimensional boundary sets of \(P\). In present paper, we extend this result to convex compact polynomial families. Examples are presented to illustrate the results.