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Avtomat. i Telemekh., 2017, Issue 11, Pages 34–47 (Mi at14673)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear Systems

Stabilization of oscillations in a coupled periodic system

V. N. Tkhai

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: Consideration was given to a model containing two coupled autonomous planar subsystems of differential equations. It was assumed that the subsystems admitted families of nondegenerate single-frequency oscillations, and coupling was described by time-periodic functions. Solved was the problem of natural stabilization of system oscillations, where by natural stabilization was meant construction of an isolated oscillation and its concurrent stabilization. Constructive conditions for smooth periodic coupling controls providing problem solution were derived. Specific control was proposed for coupled conservative systems with one degree of freedom.

Keywords: model, coupled subsystems, oscillation, stability, natural stabilization.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00587
This work was supported by the Russian Foundation for Basic Research, project no. 16-01-00587.


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English version:
Automation and Remote Control, 2017, 78:11, 1967–1977

Bibliographic databases:

PACS: 2010: 05.45.-a
MSC: 2010: 34A34, 93C10, 93D15, 93D20
Presented by the member of Editorial Board: Л. Б. Рапопорт

Received: 20.02.2017

Citation: V. N. Tkhai, “Stabilization of oscillations in a coupled periodic system”, Avtomat. i Telemekh., 2017, no. 11, 34–47; Autom. Remote Control, 78:11 (2017), 1967–1977

Citation in format AMSBIB
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\paper Stabilization of oscillations in a~coupled periodic system
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\issue 11
\pages 34--47
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\vol 78
\issue 11
\pages 1967--1977
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. N. Barabanov, V. N. Tkhai, “Natural stabilization of the oscillation in the coupled periodical system”, Eighth Polyakhov's Reading, AIP Conf. Proc., 1959, eds. E. Kustova, G. Leonov, N. Morosov, M. Yushkov, M. Mekhonoshina, Amer. Inst. Phys., 2018, 080008  crossref  isi  scopus
    2. I. N. Barabanov, V. N. Tkhai, “Stabilization of oscillations in a periodic system by choosing appropriate couplings”, Autom. Remote Control, 79:12 (2018), 2128–2135  mathnet  crossref  crossref  isi  elib
    3. V. N. Tkhai, “Periodicheskaya model, soderzhaschaya svyazannye podsistemy s razlichnymi tipami kolebanii”, Avtomat. i telemekh., 2019, no. 3, 55–67  mathnet  crossref  elib
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