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 J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 1, Pages 136–142 (Mi jsfu285)

Existence of the unique kT-periodic solution for one class of nonlinear systems

Vistoria V. Yevstafyeva

Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, Russia

Abstract: The system of ordinary differential equations with the discontinuous hysteresic nonlinearity and an external continuous biharmonic influence is considered. Sufficient conditions are obtained for existence of periodic solutions with given properties, in particular, with the period equal and multiple to the period of the external influence. We use an approach to the choice of feedback coefficients based on a nonsingular transformation of the initial system to a special canonical form. The approach allows to find analytically the switching instants and points of the image point of the required solution.

Keywords: forced periodic oscillations, nonsingular transformations, control systems, discontinuous hysteresic nonlinearity, switching instants and points.

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UDC: 517.925
Accepted: 08.11.2012
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Citation: Vistoria V. Yevstafyeva, “Existence of the unique kT-periodic solution for one class of nonlinear systems”, J. Sib. Fed. Univ. Math. Phys., 6:1 (2013), 136–142

Citation in format AMSBIB
\Bibitem{Yev13} \by Vistoria~V.~Yevstafyeva \paper Existence of the unique kT-periodic solution for one class of nonlinear systems \jour J. Sib. Fed. Univ. Math. Phys. \yr 2013 \vol 6 \issue 1 \pages 136--142 \mathnet{http://mi.mathnet.ru/jsfu285} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “Solution To Second-Order Differential Equations With Discontinuous Right-Hand Side”, Electron. J. Differ. Equ., 2014, 221
2. V. V. Yevstafyeva, “On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix”, Autom. Remote Control, 76:6 (2015), 977–988
3. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of subharmonic solutions to a hysteresis system with sinusoidal external influence”, Electron. J. Differ. Equ., 2017, 140
4. A. M. Kamachkin, D. K. Potapov, V. V. Yevstafyeva, “Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence”, Int. J. Robust Nonlinear Control, 27:2 (2017), 204–211
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