Loading [MathJax]/jax/output/SVG/config.js
Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


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




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

Sbornik: Mathematics, 2019, Volume 210, Issue 11, Pages 1511–1530
DOI: https://doi.org/10.1070/SM9154 (Mi sm9154) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Sufficient conditions for the stability of linear periodic impulsive differential equations

V. O. Bivziuka, V. I. Slyn'kobc

a University of Illinois at Urbana-Champaign, Urbana, IL, USA
b S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine, Kiev, Ukraine
c Julius-Maximilians-Universität Würzburg, Würzburg, Germany
English version PDF (542 kB) Citations (7) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM9154
Abstract: Abstract linear periodic impulsive differential equations are considered. The impulse effect instants are assumed to satisfy the average dwell-time condition (the ADT condition). The stability problem is reduced to studying the stability of an auxiliary abstract impulsive differential equation. This is a perturbed periodic impulsive differential equation, which considerably simplifies the construction of a Lyapunov function. Sufficient conditions for the asymptotic stability of abstract linear periodic impulsive differential equations are obtained. It is shown that the ADT conditions lead to less conservative dwell-time estimates guaranteeing asymptotic stability.
Bibliography: 24 titles.
Keywords: abstract linear impulsive differential equations, commutator calculus, Lyapunov stability, Lyapunov functions.
Funding agency Grant number
Ministry of Education and Science of Ukraine 0116U004691
National Academy of Sciences of Ukraine 6541230
This study was supported in part by the Ministry of Education and Science of Ukraine (project no. 0116U004691) and the National Academy of Sciences of Ukraine (budget program with budget classification code no. 6541230 “Support for the development of priority areas of scientific research”).
Received: 30.07.2018 and 25.01.2019
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: Primary 93D20; Secondary 34A37, 93B12, 93D30
Language: English
Original paper language: Russian
Citation: V. O. Bivziuk, V. I. Slyn'ko, “Sufficient conditions for the stability of linear periodic impulsive differential equations”, Sb. Math., 210:11 (2019), 1511–1530
Citation in format AMSBIB
\Bibitem{BivSly19}
\by V.~O.~Bivziuk, V.~I.~Slyn'ko
\paper Sufficient conditions for the stability of linear periodic impulsive differential equations
\jour Sb. Math.
\yr 2019
\vol 210
\issue 11
\pages 1511--1530
\mathnet{http://mi.mathnet.ru/eng/sm9154}
\crossref{https://doi.org/10.1070/SM9154}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4036799}
\zmath{https://zbmath.org/?q=an:1458.93219}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210.1511B}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000518760800001}
\elib{https://elibrary.ru/item.asp?id=46742859}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85098887336}
Linking options:
  • https://www.mathnet.ru/eng/sm9154
  • https://doi.org/10.1070/SM9154
  • https://www.mathnet.ru/eng/sm/v210/i11/p3
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:371
    Russian version PDF:91
    English version PDF:21
    References:43
    First page:12
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025