Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Asymptotic behavior of singularly perturbed systems with periodic nonlinearities and external forces. / Smirnova, Vera B.; Utina, Natalia V.; Pak, Ella E.
Proceedings of 2018 14th International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiys Conference), STAB 2018. ред. / Valentin N. Tkhai. Institute of Electrical and Electronics Engineers Inc., 2018. стр. 1-4.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - Asymptotic behavior of singularly perturbed systems with periodic nonlinearities and external forces
AU - Smirnova, Vera B.
AU - Utina, Natalia V.
AU - Pak, Ella E.
PY - 2018/7/6
Y1 - 2018/7/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85050662874&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/asymptotic-behavior-singularly-perturbed-systems-periodic-nonlinearities-external-forces
U2 - 10.1109/STAB.2018.8408402
DO - 10.1109/STAB.2018.8408402
M3 - Conference contribution
AN - SCOPUS:85050662874
SP - 1
EP - 4
BT - Proceedings of 2018 14th International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiys Conference), STAB 2018
A2 - Tkhai, Valentin N.
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference), STAB 2018
Y2 - 29 May 2018 through 31 May 2018
ER -
ID: 37032898