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On making a polynomial Hurwitz invariant by choice of feedback gains

Given a polynomial f(s,k,q) which depends on the complex variable s, a vector of design parameters k¿Rm and a vector of uncertain parameters q¿Q, we consider the following problem: Under what conditions does there exist a k* making f(s,k*,q) Hurwitz invariant? That is for all q¿Q, f(s,k*,q) has all its zeros in the strict left half plane. In this paper, we develop sufficient conditions for the existence of k* and provide a "recipe" for the construction of k* (whenever it exists). The conditions developed are seen to have an interesting control theoretic interpretation.