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Avtomatika i Telemekhanika, 2018, Issue 6, Pages 87–98 (Mi at15088)  
This article is cited in 4 scientific papers (total in 4 papers)

Topical issue

Pyragas stabilizability of unstable equilibria by nonstationary time-delayed feedback

G. A. Leonova, M. M. Shumafovb

a St. Petersburg State University, St. Petersburg, Russia
b Adyghe State University, Maikop, Russia
Full-text PDF (817 kB) Citations (4)
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Abstract: The problem of Pyragas stabilizability of unstable equilibria of nonlinear systems is considered. Stabilization algorithm by periodic time-delayed feedback is constructed. An analytical criterion for stabilization is obtained. The proposed approach is based on the method of nonstationary stabilization.
Keywords: stabilization, unstable equilibrium, nonlinear differential equation, time-delayed feedback, linearization, eigenvalues.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-2858.2018.1
This work was supported by the Grant Council at President of Russian Federation for state support of the leading scientific schools of Russian Federation for 2018–2019, project no. NSh-2858.2018.1.
Presented by the member of Editorial Board: A. P. Kurdyukov

Received: 09.11.2017
English version:
Automation and Remote Control, 2018, Volume 79, Issue 6, Pages 1029–1039
DOI: https://doi.org/10.1134/S0005117918060048
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. A. Leonov, M. M. Shumafov, “Pyragas stabilizability of unstable equilibria by nonstationary time-delayed feedback”, Avtomat. i Telemekh., 2018, no. 6, 87–98; Autom. Remote Control, 79:6 (2018), 1029–1039
Citation in format AMSBIB
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\issue 6
\pages 87--98
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\jour Autom. Remote Control
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Linking options:
  • https://www.mathnet.ru/eng/at15088
  • https://www.mathnet.ru/eng/at/y2018/i6/p87
    • This publication is cited in the following 4 articles:
    1. Shinsuke Mizukami, Keiji Konishi, Koki Yoshida, Yoshiki Sugitani, Naoyuki Hara, “Amplitude Death in Extended Time-Delay Coupled Oscillator Networks”, IEEE Access, 13 (2025), 12666  crossref
    2. M.M. Shumafov, “Leonov's Method of Nonstationary Stabilization in the Theory of Linear Control Systems”, J. Phys.: Conf. Ser., 1864:1 (2021), 012067  crossref
    3. I. V. Boykov, N. P. Krivulin, “Methods for Control of Dynamical Systems with Delayed Feedback”, J Math Sci, 255:5 (2021), 561  crossref
    4. V. E. Pastor, G. A. Gonzalez, “Oscillating delayed feedback control schemes for stabilizing equilibrium points”, Heliyon, 5:6 (2019), e01952  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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