On the existence of robust strictly positive real rational functions

A new approach for the analysis of the strict positive real property of rational functions of the form H(s)=p(s)/q(g) is proposed. This approach is based on the interlacing properties of the roots of the even and odd parts of p(s) and q(s) over the imaginary axis. From the analysis of these properties, an algorithm to obtain p(s) such that p(s)/q(s) is strictly positive real (SPR) for a given Hurwitz q(s) is developed. The problem of finding p(s) when q(s) is an uncertain Hurwitz polynomial is also considered, using this new approach. An algorithm for obtaining p(s) such that p(s)/q(s) is SPR, when q(s) has parametric uncertainties, is presented. This algorithm is easy to use and leads to p(s) in cases where previously published methods fail