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.



Why the 'S' in S-procedure/S-lemma?
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.


