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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 1, Pages 68–78 (Mi vuu519)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Weak asymptotic stability of control systems with impulsive actions

Ya. Yu. Larina

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

Abstract: We continue investigating the conditions of positive invariance and asymptotic stability of a given set relative to a control system with impulsive actions. We consider the set $\mathfrak M\doteq\{(t,x)\in[t_0,+\infty)\times\mathbb R^n\colon x\in M(t)\}$, given by a function $t\to M(t)$ that is continuous in the Hausdorff metric, where the set $M(t)$ is nonempty and compact for each $t\in\mathbb R$. In terms of the Lyapunov functions and the Clarke derivative, we obtain conditions for weak positive invariance, weak uniform Lyapunov stability and weak asymptotic stability of the set $\mathfrak M$. Also we prove a comparison theorem for solutions of systems and equations with impulses the consequence of which is the conditions for existence of solutions of the system that asymptotically tends to zero. The obtained results are illustrated by the example of model for competition of two species exposed to impulse control at given times.

Keywords: control systems with impulsive actions, Lyapunov function, weak asymptotic stability.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00346-а


DOI: https://doi.org/10.20537/vm160106

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Bibliographic databases:

UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 17.01.2016

Citation: Ya. Yu. Larina, “Weak asymptotic stability of control systems with impulsive actions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:1 (2016), 68–78

Citation in format AMSBIB
\Bibitem{Lar16}
\by Ya.~Yu.~Larina
\paper Weak asymptotic stability of control systems with impulsive actions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 1
\pages 68--78
\mathnet{http://mi.mathnet.ru/vuu519}
\crossref{https://doi.org/10.20537/vm160106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3485574}
\elib{http://elibrary.ru/item.asp?id=25681786}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
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