Geodesic
The circle criterion and Tsypkin's criterion for systems with~several nonlinearities without the use of the $S$-procedure
Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 169-182

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The circle criterion (for continuous-time systems) and Tsypkin's criterion (for discrete-time systems) of absolute stability for Lurie systems with several nonlinearities are obtained with the use of the convolution theorem and without use of the $S$-procedure. On the basis of the convolution theorem, two theorems are proved which lead to a substantial reduction in the dimension of connected systems of linear matrix inequalities. Bibliography: 19 titles.
Keywords: absolute stability of Lurie systems, matrix inequalities, circle criterion, $S$-procedure.
Mots-clés : Tsypkin's criterion 
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     title = {The circle criterion and {Tsypkin's} criterion for systems with~several nonlinearities without the use of the $S$-procedure},
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V. A. Kamenetskiy. The circle criterion and Tsypkin's criterion for systems with~several nonlinearities without the use of the $S$-procedure. Sbornik. Mathematics, Tome 215 (2024) no. 2, pp. 169-182. http://geodesic.mathdoc.fr/item/SM_2024_215_2_a2/