V. V. Yevstafyeva, “On necessary conditions for existence of periodic solutions in a dynamic system with discontinuous nonlinearity and an external periodic influence”, Ufa Math. J., 3:2 (2011), 19

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Ufa Mathematical Journal, 2011, Volume 3, Issue 2, Pages 19–26 (Mi ufa90)

This article is cited in 13 scientific papers (total in 13 papers)

On necessary conditions for existence of periodic solutions in a dynamic system with discontinuous nonlinearity and an external periodic influence

V. V. Yevstafyeva

Saint-Petersburg State University, St. Petersburg, Russia

English version PDF (347 kB) Citations (13) Russian version article

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Abstract: The system of ordinary differential equations with discontinuous nonlinearity of a non-ideal relay type and an external continuous periodic influence in the right-hand side is considered in the Euclidean space. Necessary conditions for existence of periodic solutions with given properties in problems of the specified class imposed on the coefficients of the system are obtained by means of accurate analytical methods. An approach for finding moments of time and switching points of the image point of the required solution is suggested in the case when the period of the solution is multiple to the period of the function describing the external perturbation.

Keywords: switching points, forced periodic oscillations, automatic control systems, discontinuous hysteresis nonlinearity.

Received: 18.01.2011

Bibliographic databases:

Document Type: Article

UDC: 517.925

Language: English

Original paper language: Russian

Citation: V. V. Yevstafyeva, “On necessary conditions for existence of periodic solutions in a dynamic system with discontinuous nonlinearity and an external periodic influence”, Ufa Math. J., 3:2 (2011), 19–26

Citation in format AMSBIB

\Bibitem{Yev11}

\by V.~V.~Yevstafyeva

\paper On necessary conditions for existence of periodic solutions in a~dynamic system with discontinuous nonlinearity and an external periodic influence

\jour Ufa Math. J.

\yr 2011

\vol 3

\issue 2

\pages 19--26

\mathnet{http://mi.mathnet.ru/eng/ufa90}

\zmath{https://zbmath.org/?q=an:1249.34175}

Linking options:

https://www.mathnet.ru/eng/ufa90

https://www.mathnet.ru/eng/ufa/v3/i2/p20

This publication is cited in the following 13 articles:

V. V. Yevstafyeva, “Control design for a perturbed system with an ambiguous nonlinearity”, Autom. Remote Control, 84:3 (2023), 254–269
V. V. Yevstafyeva, “Existence of $T/k$ -Periodic Solutions of a Nonlinear Nonautonomous System Whose Matrix Has a Multiple Eigenvalue”, Math. Notes, 109:4 (2021), 551–562
Yevstafyeva V.V., “Existence of Two-Point Oscillatory Solutions of a Relay Nonautonomous System With Multiple Eigenvalue of a Real Symmetric Matrix”, Ukr. Math. J., 73:5 (2021), 746–757
Yevstafyeva V.V., “On the Existence of Two-Point Oscillatory Solutions of a Perturbed Relay System With Hysteresis”, Differ. Equ., 57:2 (2021), 155–164
A. M. Kamachkin, D. K. Potapov, V. V. Evstafeva, “Dinamika i sinkhronizatsiya tsiklicheskikh struktur ostsillyatorov s gisterezisnoi obratnoi svyazyu”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 16:2 (2020), 186–199
Yevstafyeva V.V., “Periodic Solutions of a System of Differential Equations With Hysteresis Nonlinearity in the Presence of Eigenvalue Zero”, Ukr. Math. J., 70:8 (2019), 1252–1263
A. M. Kamachkin, G. M. Khitrov, V. N. Shamberov, “Normalnye formy matrits v zadachakh dekompozitsii i upravleniya mnogomernykh sistem”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 13:4 (2017), 417–430
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “On Uniqueness and Properties of Periodic Solution of Second-Order Nonautonomous System With Discontinuous Nonlinearity”, J. Dyn. Control Syst., 23:4 (2017), 825–837
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “Existence of Subharmonic Solutions to a Hysteresis System With Sinusoidal External Influence”, Electron. J. Differ. Equ., 2017, 140
Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “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
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
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
Vistoria V. Yevstafyeva, “Existence of the unique kT-periodic solution for one class of nonlinear systems”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 136–142

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	452
Russian version PDF:	141
English version PDF:	44
References:	85
First page:	2

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