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Let P be a convex set of real polynomials. Consideration is given to the question of when there exists a real polynomial b(s), or more generally, a real transfer function b(s), such that p(s)/b(s) is strictly positive real for all p(s) in P. Necessary and sufficient conditions are found for the transfer function b(s) case, and when the degree of the polynomials in P is restricted, such conditions are also found for the polynomial b(s) case. Closely related results are also obtained for a z-transform version of the problem. The results have application in adaptive systems.>
Anderson et al. (Sun,) studied this question.