RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki:
Year:
Volume:
Issue:
Page:
Find






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


Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 1, Pages 51–59 (Mi vuu464)  

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

MATHEMATICS

Lyapunov functions and comparison theorems for control systems with impulsive actions

Ya. Yu. Larina

Department of Mathematical Analysis, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: We extend the results of E. L. Tonkov and E. A. Panasenko to differential equations and control systems with impulsive actions. In terms of Lyapunov functions and the Clarke derivative we obtain comparison theorems for systems with impulsive effect. We consider the set $\mathfrak M\doteq\{(t,x)\in[t_0,+\infty)\times\mathbb R^n\colon x\in M(t)\}$, defined by continuous function $t\to M(t)$, where for every $t\in\mathbb R$ the set $M(t)$ is nonempty and compact. We obtain conditions for the positive invariance of this set, the uniform Lyapunov stability and the uniform asymptotic stability. We make a comparison with the researches of other authors who have considered the zero solution stability for similar systems.

Keywords: control systems with impulsive actions, Lyapunov function, differential inclusions.

Full text: PDF file (212 kB)
References: PDF file   HTML file
UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 17.02.2015

Citation: Ya. Yu. Larina, “Lyapunov functions and comparison theorems for control systems with impulsive actions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:1 (2015), 51–59

Citation in format AMSBIB
\Bibitem{Lar15}
\by Ya.~Yu.~Larina
\paper Lyapunov functions and comparison theorems for control systems with impulsive actions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 1
\pages 51--59
\mathnet{http://mi.mathnet.ru/vuu464}
\elib{http://elibrary.ru/item.asp?id=23142051}


Linking options:
  • http://mi.mathnet.ru/eng/vuu464
  • http://mi.mathnet.ru/eng/vuu/v25/i1/p51

    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. Ya. Yu. Larina, “Statisticheskie kharakteristiki upravlyaemykh sistem s impulsnym vozdeistviem”, Izv. IMI UdGU, 2015, no. 2(46), 99–105  mathnet  elib
    2. Ya. Yu. Larina, “O slaboi asimptoticheskoi ustoichivosti upravlyaemykh sistem s impulsnym vozdeistviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:1 (2016), 68–78  mathnet  crossref  mathscinet  elib
    3. Ya. Yu. Larina, L. I. Rodina, “Asimptoticheski ustoichivye mnozhestva upravlyaemykh sistem s impulsnym vozdeistviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:4 (2016), 490–502  mathnet  crossref  mathscinet  elib
    4. L. I. Rodina, “On asymptotic properties of solutions of control systems with random parameters”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S144–S153  mathnet  crossref  crossref  isi  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
    Number of views:
    This page:164
    Full text:72
    References:34

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