Asymptotic behavior of singularly perturbed systems with periodic nonlinearities and external forces

Vera B. Smirnova, Natalia V. Utina, Ella E. Pak

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

In this paper we consider singularly perturbed phase synchronization systems with external disturbances. The systems are described by integro-differential Volterra equations with periodic nonlinear functions and a small parameter at the higher derivative. The disturbed systems examined in this paper have (like undisturbed ones) infinite sequence of equilibrium points. So for them the main problem of phase synchronization systems remains: whether the system is gradient-like, i.e. its any solution converges to one of equilibria. In this paper we offer frequency-algebraic criteria which guarantee that the convergence of any solution of undisturbed system under singular perturbation is not destroyed by external disturbance. If the system is not gradient-like it may have periodic solutions. We demonstrate that the relaxation of frequency-algebraic criteria leads to conditions for the absence of high frequency periodic solutions. The results of the investigation are uniform with respect to the small parameter.

Язык оригиналаанглийский
Название основной публикацииProceedings of 2018 14th International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiys Conference), STAB 2018
РедакторыValentin N. Tkhai
ИздательInstitute of Electrical and Electronics Engineers Inc.
Страницы1-4
Число страниц4
ISBN (электронное издание)9781538645567
DOI
СостояниеОпубликовано - 6 июл 2018
Событие14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference), STAB 2018 - Moscow, Российская Федерация
Продолжительность: 29 мая 201831 мая 2018

Конференция

Конференция14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference), STAB 2018
СтранаРоссийская Федерация
ГородMoscow
Период29/05/1831/05/18

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Smirnova, V. B., Utina, N. V., & Pak, E. E. (2018). Asymptotic behavior of singularly perturbed systems with periodic nonlinearities and external forces. В V. N. Tkhai (Ред.), Proceedings of 2018 14th International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiys Conference), STAB 2018 (стр. 1-4). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/STAB.2018.8408402