Synthesis of positive real feedback systems: a simple derivation via Parrott´s theorem

A simple derivation of the formulas for controller rendering a closed-loop system strongly positive real is presented. The derivation is based on Parrott´s theorem and the positive real lemma. When the positive real lemma is applied to the closed loop system, a bilinear matrix inequality results. The significance of Parrott´s theorem in the context of a strongly positive real synthesis problem is that it allows one to convert this bilinear matrix inequality into two linear matrix inequalities