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.
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Gusev et al. (2006) studied this question.
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