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Avtomatika i Telemekhanika, 2019, Issue 12, Pages 47–58
DOI: https://doi.org/10.1134/S0005231019120031 (Mi at15259) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Nonlinear Systems

Oscillations of a coupled controlled system near equilibrium

I. N. Barabanov, V. N. Tkhai

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (627 kB) Citations (2)
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DOI: https://doi.org/10.1134/S0005231019120031
Abstract: A nonlinear autonomous system near an equilibrium is considered. The matrix of its linearized counterpart is supposed to have imaginary eigenvalues without internal resonances up to the fourth order inclusive. The oscillations of this system caused by periodic controls with a small gain $k$ are investigated, and isolated resonant oscillations are found. The amplitudes of the oscillations in terms of the parameter $k$ are estimated, and their stability is analyzed. It is shown that the existence of a resonant oscillation is guaranteed by the control action, while its asymptotic stability is determined by the uncontrolled system.
Keywords: nonlinear coupled system, equilibrium, resonance, periodic control, oscillation, stability.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00146
This work was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00146.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 28.03.2019
Revised: 12.04.2019
Accepted: 25.04.2019
English version:
Automation and Remote Control, 2019, Volume 80, Issue 12, Pages 2126–2134
DOI: https://doi.org/10.1134/S0005117919120038
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. N. Barabanov, V. N. Tkhai, “Oscillations of a coupled controlled system near equilibrium”, Avtomat. i Telemekh., 2019, no. 12, 47–58; Autom. Remote Control, 80:12 (2019), 2126–2134
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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