Robust Strict Positive Realness: Characterization and Construction

Let 풫 be a convex set of real polynomials. This paper considers the question of when there exists a real polynomial bis), or more generally, a real transfer function b(s), such that p(s)/b(s) is strictly positive real for all p(s)ϵ 풫. Necessary and sufficient conditions are found for the transfer function b(s) case, and when the degree of the polynomials in 풫 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.