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Русская версия

**A. I. Shepeljavyi**

RUSSIA, 198904, Saint-Petersburg, Petrodvorets, Universitetsky pr., 28,

Saint-Petersburg State University,

faculty of mathematics amd mechanics

**V. B. Smirnova**

RUSSIA, 198904, Saint-Petersburg, Petrodvorets, Universitetsky pr., 28,

Saint-Petersburg State University,

faculty of mathematics amd mechanics

**N. V. Utina**

RUSSIA, 198904, Saint-Petersburg, Petrodvorets, Universitetsky pr., 28,

Saint-Petersburg State University,

faculty of mathematics amd mechanics

Discrete contol system with a periodic nonlinearity is considered. Its important feature is the number of cycle-slipping of the transient regime. In the paper by means of Lyapunov direct method and Bakaev-Guzh technique for differentiable functions the estimation of the number of cycle--slipping is established. Yakubovich--Kalman theorem is also used. Therefore the main theorem of the paper is formulated as a frequency-domain criterion.