Two-Riccati positive real synthesis: LMI approach

Abstract

A simple derivation of the two Riccati formulae for controllers rendering a closed loop system strongly positive real is presented. We also show how the bounded real synthesis problem expressed as a bilinear matrix inequality (BMI) can be derived from the positive real synthesis BMI via a bilinear transformation, and how the two Riccati inequality solutions for the positive real synthesis problem can be derived from the two Riccati inequality solution for the bounded real synthesis problem via a bilinear transformation, and vice versa.