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

This article is cited in 4 scientific papers (total in 4 papers)

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.

Full text: PDF file (170 kB)
References: PDF file   HTML file
UDC: 517.925
Received: 10.06.2012
Received in revised form: 08.10.2012
Accepted: 08.11.2012
Language:

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  mathscinet  zmath  isi  elib
    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  mathnet  crossref  isi  elib  elib
    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  mathscinet  zmath  isi
    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  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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