On the design of strictly positive real transfer functions

The synthesis of strictly positive real transfer functions is considered. For a given Hurwitz polynomial of degree n comprising the denominator polynomial, necessary and sufficient conditions on the numerator which render a rational function strictly positive real are given. In the case where the function is strictly proper, a parameterization of the polynomial numerator by n real numbers satisfying a simple constraint is provided. The approach taken employs factorization of a polynomial into its even and odd parts. The relationship of the results to those provided by the Kalman-Yakubovich lemma is given and the present method shown to have certain advantages