Let P be a set of real polynomials of degree n. Set P can be identified with some subset P of Rn consists of vectors of coefficients of P. If P as 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 polonomial families. Examples are presented to illustrate the results.