Generalized S-Procedure and Finite Frequency KYP Lemma

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.