Kalman-Popov-Yakubovich lemma and the S-procedure: A historical essay

Authors:
S. V. Gusev;A. L. Likhtarnikov
Affiliations:
St. Petersburg State University, St. Petersburg, Russia;St. Petersburg State University, St. Petersburg, Russia
Venue:
Automation and Remote Control
Year:
2006

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Abstract

A history of two fundamental results of the mathematical system theory--the Kalman-Popov-Yakubovich lemma and the theorem of losslessness of the S-procedure--was presented. The studies directly concerned with these statements were reviewed. The recent publications using the theorem of losslessness of the S-procedure to derive the Kalman-Popov-Yakubovich lemma and its generalizations were analyzed.