Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 305-320

Generalized S-procedure and finite frequency KYP lemma

Tetsuya Iwasaki,1 Gjerrit Meinsma,2 and Minyue Fu3

1Department of Control Systems Engineering, Tokyo Institute of Technology, 2-12-1 Oookayama, Meguro, Tokyo 152, Japan
2Department of Systems, Signals and Control, Faculty of Mathematical Sciences, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
3Department of Electrical and Computer Engineering, University of Newcastle, Callaghan NSW 2308, Australia

Received 14 December 1998

Copyright © 2000 Tetsuya Iwasaki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.