RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2008, Volume 84, Issue 6, Pages 888–906 (Mi mz4052)  

This article is cited in 4 scientific papers (total in 4 papers)

Development of the Direct Lyapunov Method for Functional-Differential Equations with Infinite Delay

N. O. Sedova

Ulyanovsk State University

Abstract: We propose new sufficient conditions for the uniform asymptotic stability of the zero solution of a retarded functional-differential equation with unbounded (infinite) delay. The equation can be nonlinear and nonautonomous. The conditions are formulated in terms of Razumikhin-type functions, and in this case, a function is coupled with a functional related to this function by a certain dependence. In the results presented here, because of additional restrictions imposed on the right-hand side of the equation and the use of the limiting equation techniques, the classical requirements stating that the function and its derivative must be of fixed sign along the solution are weakened to the requirements that the function and its derivative must be of constant signs.

Keywords: retarded functional-differential equation, zero solution, infinite delay, uniform asymptotic stability, separability, phase space, Arzelà theorem

DOI: https://doi.org/10.4213/mzm4052

Full text: PDF file (592 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2008, 84:6, 825–841

Bibliographic databases:

UDC: 517.929.4
Received: 23.05.2007
Revised: 12.02.2008

Citation: N. O. Sedova, “Development of the Direct Lyapunov Method for Functional-Differential Equations with Infinite Delay”, Mat. Zametki, 84:6 (2008), 888–906; Math. Notes, 84:6 (2008), 825–841

Citation in format AMSBIB
\Bibitem{Sed08}
\by N.~O.~Sedova
\paper Development of the Direct Lyapunov Method for Functional-Differential Equations with Infinite Delay
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 6
\pages 888--906
\mathnet{http://mi.mathnet.ru/mz4052}
\crossref{https://doi.org/10.4213/mzm4052}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2492804}
\transl
\jour Math. Notes
\yr 2008
\vol 84
\issue 6
\pages 825--841
\crossref{https://doi.org/10.1134/S0001434608110266}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000262855600026}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59749098616}


Linking options:
  • http://mi.mathnet.ru/eng/mz4052
  • https://doi.org/10.4213/mzm4052
  • http://mi.mathnet.ru/eng/mz/v84/i6/p888

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. N. O. Sedova, “Stability in systems with unbounded aftereffect”, Autom. Remote Control, 70:9 (2009), 1553–1564  mathnet  crossref  mathscinet  zmath  isi
    2. Druzhinina O.V., Sedova N.O., “Method of Limiting Equations For the Stability Analysis of Equations With Infinite Delay in the Carath,Odory Conditions: i”, Differ. Equ., 50:5 (2014), 569–580  crossref  mathscinet  zmath  isi  scopus
    3. Pham Huu Anh Ngoc, Cao Thanh Tinh, “Explicit criteria for exponential stability of time-varying systems with infinite delay”, Math. Control Signal Syst., 28:1 (2016), 4  crossref  mathscinet  isi  scopus
    4. A. S. Andreev, N. O. Sedova, “The method of Lyapunov–Razumikhin functions in stability analysis of systems with delay”, Autom. Remote Control, 80:7 (2019), 1185–1229  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
    Number of views:
    This page:318
    Full text:115
    References:26
    First page:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020