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Leonov’s method of nonlocal reduction and its further development. / Smirnova, Vera B. ; Proskurnikov, Anton V. .

European Control Conference 2020, ECC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 94-99 9143744.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Smirnova, VB & Proskurnikov, AV 2020, Leonov’s method of nonlocal reduction and its further development. in European Control Conference 2020, ECC 2020., 9143744, Institute of Electrical and Electronics Engineers Inc., pp. 94-99, 19th European Control Conference, ECC 2020, Saint Petersburg, Russian Federation, 12/05/20. https://doi.org/10.23919/ECC51009.2020.9143744

APA

Smirnova, V. B., & Proskurnikov, A. V. (2020). Leonov’s method of nonlocal reduction and its further development. In European Control Conference 2020, ECC 2020 (pp. 94-99). [9143744] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ECC51009.2020.9143744

Vancouver

Smirnova VB, Proskurnikov AV. Leonov’s method of nonlocal reduction and its further development. In European Control Conference 2020, ECC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 94-99. 9143744 https://doi.org/10.23919/ECC51009.2020.9143744

Author

Smirnova, Vera B. ; Proskurnikov, Anton V. . / Leonov’s method of nonlocal reduction and its further development. European Control Conference 2020, ECC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. pp. 94-99

BibTeX

@inproceedings{9f35b80376af418ebd7d8147fc6ffb6c,
title = "Leonov{\textquoteright}s method of nonlocal reduction and its further development",
abstract = "The method of nonlocal reduction has been proposed by G.A. Leonov in the 1980s for stability analysis of nonlinear feedback systems. The method combines the comparison principle with Lyapunov techniques. A feedback system is investigated via its reduction to a simpler {"}comparison{"} system, whose dynamics can be studied efficiently. The trajectories of the comparison system are explicitly used in the design of Lyapunov functions. Leonov's method proves to be an efficient tool for analysis of Lur'e-type systems with periodic nonlinearities and infinite sets of equilibria. In this paper, we further refine the nonlocal reduction method for periodic systems and obtain new sufficient frequency-algebraic conditions ensuring the convergence of every solution to some equilibrium point (gradient-like behavior).",
keywords = "Lagrange stability, Lyapunov function, Nonlinear system, periodic nonlinearity",
author = "Smirnova, {Vera B.} and Proskurnikov, {Anton V.}",
note = "Publisher Copyright: {\textcopyright} 2020 EUCA.; 19th European Control Conference, ECC 2020 ; Conference date: 12-05-2020 Through 15-05-2020",
year = "2020",
month = may,
doi = "10.23919/ECC51009.2020.9143744",
language = "English",
isbn = "978-1-7281-8813-3",
pages = "94--99",
booktitle = "European Control Conference 2020, ECC 2020",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "United States",
url = "https://ecc20.eu/",

}

RIS

TY - GEN

T1 - Leonov’s method of nonlocal reduction and its further development

AU - Smirnova, Vera B.

AU - Proskurnikov, Anton V.

N1 - Publisher Copyright: © 2020 EUCA.

PY - 2020/5

Y1 - 2020/5

N2 - The method of nonlocal reduction has been proposed by G.A. Leonov in the 1980s for stability analysis of nonlinear feedback systems. The method combines the comparison principle with Lyapunov techniques. A feedback system is investigated via its reduction to a simpler "comparison" system, whose dynamics can be studied efficiently. The trajectories of the comparison system are explicitly used in the design of Lyapunov functions. Leonov's method proves to be an efficient tool for analysis of Lur'e-type systems with periodic nonlinearities and infinite sets of equilibria. In this paper, we further refine the nonlocal reduction method for periodic systems and obtain new sufficient frequency-algebraic conditions ensuring the convergence of every solution to some equilibrium point (gradient-like behavior).

AB - The method of nonlocal reduction has been proposed by G.A. Leonov in the 1980s for stability analysis of nonlinear feedback systems. The method combines the comparison principle with Lyapunov techniques. A feedback system is investigated via its reduction to a simpler "comparison" system, whose dynamics can be studied efficiently. The trajectories of the comparison system are explicitly used in the design of Lyapunov functions. Leonov's method proves to be an efficient tool for analysis of Lur'e-type systems with periodic nonlinearities and infinite sets of equilibria. In this paper, we further refine the nonlocal reduction method for periodic systems and obtain new sufficient frequency-algebraic conditions ensuring the convergence of every solution to some equilibrium point (gradient-like behavior).

KW - Lagrange stability

KW - Lyapunov function

KW - Nonlinear system

KW - periodic nonlinearity

UR - https://ieeexplore.ieee.org/document/9143744

UR - http://www.scopus.com/inward/record.url?scp=85090140221&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/fd9f8330-fdd3-3389-99a1-112615efb21b/

U2 - 10.23919/ECC51009.2020.9143744

DO - 10.23919/ECC51009.2020.9143744

M3 - Conference contribution

SN - 978-1-7281-8813-3

SP - 94

EP - 99

BT - European Control Conference 2020, ECC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 19th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -

ID: 71428679