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

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

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
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} 

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

 SHARE:

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
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
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
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
•  Number of views: This page: 318 Full text: 115 References: 26 First page: 10