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Avtomatika i Telemekhanika, 2006, Issue 9, Pages 3–14 (Mi at1230)  
This article is cited in 20 scientific papers (total in 20 papers)

Deterministic Systems

On stability of the solutions of a class of nonlinear delay systems

A. Yu. Aleksandrov, A. P. Zhabko

Saint-Petersburg State University
Full-text PDF (219 kB) Citations (20)
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Abstract: Consideration was given to a class of systems of nonlinear differential equations with retarded argument. It was assumed that in the absence of delay the zero solutions of the systems under study are asymptotically stable. Using the method of Lyapunov functions in the form of B. S. Razumikhin, it was proved that if the right-hand sides of these equations are free of the linear terms relative to the phase variables, then the asymptotic stability is retained for any delay.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 06.10.2005
English version:
Automation and Remote Control, 2006, Volume 67, Issue 9, Pages 1355–1365
DOI: https://doi.org/10.1134/S0005117906090013
Bibliographic databases:
Document Type: Article
PACS: 02.30.Ks, 02.30.Yy
Language: Russian
Citation: A. Yu. Aleksandrov, A. P. Zhabko, “On stability of the solutions of a class of nonlinear delay systems”, Avtomat. i Telemekh., 2006, no. 9, 3–14; Autom. Remote Control, 67:9 (2006), 1355–1365
Citation in format AMSBIB
\Bibitem{AleZha06}
\by A.~Yu.~Aleksandrov, A.~P.~Zhabko
\paper On stability of the solutions of a~class of nonlinear delay systems
\jour Avtomat. i Telemekh.
\yr 2006
\issue 9
\pages 3--14
\mathnet{http://mi.mathnet.ru/at1230}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2266466}
\zmath{https://zbmath.org/?q=an:1194.34139}
\transl
\jour Autom. Remote Control
\yr 2006
\vol 67
\issue 9
\pages 1355--1365
\crossref{https://doi.org/10.1134/S0005117906090013}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749039463}
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :107
    References:58
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