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

European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.. 2020. 19809533.

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 (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.., 19809533, 19th European Control Conference, ECC 2020, Saint Petersburg, Russian Federation, 12/05/20.

APA

Smirnova, V. B., & Proskurnikov, A. V. (Accepted/In press). Leonov's method of nonlocal reduction and its further development. In European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020. [19809533]

Vancouver

Smirnova VB, Proskurnikov AV. Leonov's method of nonlocal reduction and its further development. In European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.. 2020. 19809533

Author

Smirnova, Vera B. ; Proskurnikov, Anton V. / Leonov's method of nonlocal reduction and its further development. European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.. 2020.

BibTeX

@inproceedings{377731325195418dbf5ae19ca346fddf,
title = "Leonov'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 {"}compar-ison{"} 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 = "Stability criteria, Circuit stability, synchronization, Lyapunov methods, Trajectory, nonlinear system, periodic nonlinearity, Lagrange stability, Lyapunov function",
author = "Smirnova, {Vera B.} and Proskurnikov, {Anton V.}",
year = "2020",
language = "English",
isbn = "9781728188133",
booktitle = "European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.",
note = "19th European Control Conference, ECC 2020 ; Conference date: 12-05-2020 Through 15-05-2020",
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.

PY - 2020

Y1 - 2020

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 "compar-ison" 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 "compar-ison" 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 - Stability criteria

KW - Circuit stability

KW - synchronization

KW - Lyapunov methods

KW - Trajectory

KW - nonlinear system

KW - periodic nonlinearity

KW - Lagrange stability

KW - Lyapunov function

UR - https://www.researchgate.net/publication/339586768_Leonov's_method_of_nonlocal_reduction_and_its_further_development

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

M3 - Conference contribution

SN - 9781728188133

BT - European Control Conference (ECC 2020), Saint Petersburg, Russia, May 12-15, 2020.

T2 - 19th European Control Conference, ECC 2020

Y2 - 12 May 2020 through 15 May 2020

ER -

ID: 50933351