Sufficient conditions for asymptotic stability of linear autonomous impulsive systems
type: Item
instance of: scholarly article
title: Sufficient conditions for asymptotic stability of linear autonomous impulsive systems
zbMATH Open document ID: 0931.34030
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-02-14T00:00:00Z
full work available at URL: CONT28-4.html
review text: The author investigates the asymptotic stability of a linear system of differential equations with impulses \[ x'(t)=Ax(t),\quad t\neq t_{k},\;t\geq t_{0} \qquad \quad x(t_{k}^{+})=C x(t_{k}), \] where \(A\) and \(C\) are constant \((n\times n)\)-matrices, \(C\) invertible. In the particular case when \(A\) and \(C\) are diagonalizable, an easily verifiable condition is given to assure the asymptotic stability of the system. For the general situation, a sufficient condition is proved by using the method of quasidiagonalization. Two interesting examples are worked out to illustrate the applicability of the main results and to discuss some relevant facts about remarkable aspects of such results.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1309885
zbMATH Keywords: systems of differential equations with impulses
zbMATH Keywords: asymptotic stability
author: Raúl Naulin
MaRDI profile type: Publication
OpenAlex ID: W1982282420
cites work: Q3993076
cites work: Q4003924
cites work: Q5822220
cites work: Q5565859
cites work: Q3995625
cites work: Dichotomies for systems with discontinuous coefficients
cites work: Quasi-diagonalization of linear impulsive systems and applications
cites work: Q4333483
cites work: Q4095239
DOI: 10.1216/RMJM/1181071723
description: scientific article; zbMATH DE number 1309885