$H_{\infty }$ Controller Design Using an Alternative to Youla Parameterization

All H_∞ controllers of a SISO LTI system are parameterized thanks to the relation between Bounded Real Lemma and Positive Real Lemma. This new parameterization shares the same features with Youla parameterization, namely on the convexity of H_∞ norm constraints for the closed-loop transfer functions. However, it can deal with low-order controllers and can be extended easily for the systems with polytopic uncertainty. The effectiveness of the proposed method is shown via an academic example.