Generalized <i>S</i>‐procedure and finite frequency KYP lemma

Abstract

The contribution of this paper is twofold. First we give a generalization of the S ‐procedure which has been proven useful for robustness analysis of control systems. We then apply the generalized S ‐procedure to derive an extension of the Kalman – Yakubovich – Popov lemma that converts a frequency domain condition within a finite interval to a linear matrix inequality condition suitable for numerical computations.