The Development of Lyapunov Direct Method in Application to Synchronization Systems

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The Development of Lyapunov Direct Method in Application to Synchronization Systems. / Smirnova, Vera B. ; Proskurnikov, Anton V. ; Utina, Natalia V. .

In: Journal of Physics: Conference Series, Vol. 1864, No. 1, 012065, 2021.

Research output: Contribution to journal › Conference article › peer-review

Author

Smirnova, Vera B. ; Proskurnikov, Anton V. ; Utina, Natalia V. . / The Development of Lyapunov Direct Method in Application to Synchronization Systems. In: Journal of Physics: Conference Series. 2021 ; Vol. 1864, No. 1.

BibTeX

@article{cd40318f18ae4f5295a2d9bc8047c140,

title = "The Development of Lyapunov Direct Method in Application to Synchronization Systems",

abstract = "The paper is devoted to asymptotic behavior of synchronization systems, i.e. Lur'e–type systems with periodic nonlinearities and infinite sets of equilibrum. This class of systems can not be efficiently investigated by standard Lyapunov functions. That is why for synchronization systems several new methods have been elaborated in the framework of Lyapunov direct method. Two of them: the method of periodic Lyapunov functions and the nonlocal reduction method, proved to be rather efficient. In this paper we combine these two methods and the Kalman-Yakubovich-Popov lemma to obtain new frequency–algebraic criteria ensuring Lagrange stability and the convergence of solutions.",

keywords = "Lur'e--type system, periodic nonlinearity, Lyapunov--type function, Lagrange stability, gradient--like behavior",

author = "Smirnova, {Vera B.} and Proskurnikov, {Anton V.} and Utina, {Natalia V.}",

note = "Publisher Copyright: {\textcopyright} Published under licence by IOP Publishing Ltd.; 13th Multiconference on Control Problems, MCCP 2020 ; Conference date: 06-10-2020 Through 08-10-2020",

year = "2021",

doi = "10.1088/1742-6596/1864/1/012065",

language = "English",

volume = "1864",

journal = "Journal of Physics: Conference Series",

issn = "1742-6588",

publisher = "IOP Publishing Ltd.",

number = "1",

url = "http://www.elektropribor.spb.ru/nauchnaya-deyatelnost/xiii-mkpu/index3.php",

}

RIS

TY - JOUR

T1 - The Development of Lyapunov Direct Method in Application to Synchronization Systems

AU - Smirnova, Vera B.

AU - Proskurnikov, Anton V.

AU - Utina, Natalia V.

N1 - Conference code: 13

PY - 2021

Y1 - 2021

N2 - The paper is devoted to asymptotic behavior of synchronization systems, i.e. Lur'e–type systems with periodic nonlinearities and infinite sets of equilibrum. This class of systems can not be efficiently investigated by standard Lyapunov functions. That is why for synchronization systems several new methods have been elaborated in the framework of Lyapunov direct method. Two of them: the method of periodic Lyapunov functions and the nonlocal reduction method, proved to be rather efficient. In this paper we combine these two methods and the Kalman-Yakubovich-Popov lemma to obtain new frequency–algebraic criteria ensuring Lagrange stability and the convergence of solutions.

AB - The paper is devoted to asymptotic behavior of synchronization systems, i.e. Lur'e–type systems with periodic nonlinearities and infinite sets of equilibrum. This class of systems can not be efficiently investigated by standard Lyapunov functions. That is why for synchronization systems several new methods have been elaborated in the framework of Lyapunov direct method. Two of them: the method of periodic Lyapunov functions and the nonlocal reduction method, proved to be rather efficient. In this paper we combine these two methods and the Kalman-Yakubovich-Popov lemma to obtain new frequency–algebraic criteria ensuring Lagrange stability and the convergence of solutions.

KW - Lur'e--type system, periodic nonlinearity, Lyapunov--type function, Lagrange stability, gradient--like behavior

UR - http://www.scopus.com/inward/record.url?scp=85107433199&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/05bdcb58-ab00-3831-90e5-f4f3b9f87ab9/

U2 - 10.1088/1742-6596/1864/1/012065

DO - 10.1088/1742-6596/1864/1/012065

M3 - Conference article

VL - 1864

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012065

T2 - 13th Multiconference on Control Problems, MCCP 2020

Y2 - 6 October 2020 through 8 October 2020

ER -

ID: 86202152