Why the 'S' in S-procedure/S-lemma? The S-procedure (also called as S-lemma) is a technique from V. A. Yakubovich that is used to relax a system of quadratic inequalities to a linear matrix inequality problem. It is used largely in control and optimization: a review of it is given in [1] and [2].
Does anyone know why the S-procedure is called this way? Is there a reason for why the letter 'S' in S-procedure? Unfortunately, I don't have access to the original paper ([3]) from Yakubovich.
References:
[1]: Derinkuyu, Kürşad, and Mustafa Ç. Pınar. "On the S-procedure and some variants." Mathematical Methods of Operations Research 64.1 (2006): 55-77.
[2]: Pólik, Imre, and Tamás Terlaky. "A survey of the S-lemma." SIAM review 49.3 (2007): 371-418.
[3]: Yakubovich, V. A. "S-procedure in nonlinear control theory." Vestnik Leningrad University: Mathematics 1 (1971): 62-77.
 A: According to [1] the term S procedure was coined in 1964 by Aizerman in the book Absolute stability of regulator systems. This book is available through amazon and in various libraries. Given the title of the book I'm inclined to say that the name S procedure is related to the stability of some system of inequalities 
[1] El Ghaoui, Laurent, Eric Feron, and Venkataramanan Balakrishnan. Linear matrix inequalities in system and control theory. Vol. 15. Philadelphia: Society for industrial and applied mathematics, 1994.
A: The paper http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=at&paperid=1299&option_lang=eng by Gusev and Likhtarnikov, which appeared in English translation at http://link.springer.com/article/10.1134%2FS000511790611004X, says on page 9 of the original paper (in Russian) that the letter $S$ is used as the name of a function 
$S(x,\xi) = V'(x,\xi) + \tau\sigma{f(\sigma)}$ in the book Absolute Stability of Regulator Systems by Aizerman and Gantmakher, published by the Soviet Academy of Sciences in 1963. (This is the original book mentioned by user3429697, but appearing a year earlier than its English translation. Note the book has two authors, not one.) Gusev and Likhtarnikov say that the computations in which $S(x,\xi)$ arose generalized an approach introduced in a book by A. I. Lurie, "Some Nonlinear Problems in the Theory of Automatic Control" (Gostekhizdat, 1951), who used the same function with $\tau = 1$, and since Aizerman and Gantmakher write the function as $S$ they named the process of Lurie the $S$-procedure.
