An alternative to the Youla parameterization for H∞ controller design

All ℋ_∞ controllers of a SISO LTI system are parameterized thanks to the relation between the Bounded Real Lemma and the Positive Real Lemma. This new parameterization shares the features of Youla parameterization, namely the convexity of ℋ_∞ norm constraints for the closed-loop transfer functions. However, by contrast to Youla parameterization, it can deal with any controller order and any controller structure, e.g. PID controllers. Moreover, it can be easily used for systems with polytopic uncertainty. For polytopic systems, the proposed parameterization provides a convex inner approximation of the set of all ℋ_∞ controllers, which can be enlarged by increasing the controller order. The effectiveness of the proposed method is shown via simulation results.