An extension of a uniform asymptotic stability theorem by Matrosov
type: Item
instance of: scholarly article
title: An extension of a uniform asymptotic stability theorem by Matrosov
zbMATH Open document ID: 0642.34052
author: Teruyo Wada
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: The purpose of this paper is to extend Theorem 1.2 in the paper by \textit{V. M. Matrosov} [(*) J. Appl. Math. Mech. 26, 1337-1353 (1962; Zbl 0123.054)] and to obtain sufficient conditions for uniform asymptotic stability of solutions of ordinary differential equations. Since several conditions in this paper are incorrect, the author would like to correct them in the following way. The conditions (iii), (iii') and (iii'') should be replaced by the following (iii), (iii') and (iii''), respectively. (iii) The family \({\mathcal U}=\{U(\cdot,u(\cdot))+u(\cdot)\) is any continuous function from \({\mathbb{R}}^+\) into \(B_{H\cdot}\}\) is equicontinuous on \({\mathfrak R}^+\). (iii') The family \({\mathcal V}=\{\dot V_{(1)}(\cdot,u(\cdot):u(\cdot)\) is any continuous function from \({\mathbb{R}}^+\) into \(B_{H\cdot}\}\) is equicontinuous on \({\mathfrak R}^+\). (iii'') Let \(A(t,x)\equiv \dot V_{(1)}(t,x)\). \(\dot A_{(1)}(t,x)\) is bounded on \({\mathfrak R}+;\times B_{H\cdot}\). Corollary 2 includes Theorem 1.2 of (*) as a special case.
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4046198
zbMATH Keywords: Lyapunov function
zbMATH Keywords: uniform asymptotic stability
MaRDI profile type: Publication
full work available at URL: pjaa.63.350
OpenAlex ID: W1994571040
cites work: Q3946471
cites work: On the stability of motion
cites work: Stability theory by Liapunov's direct method
DOI: 10.3792/PJAA.63.350
description: scientific article; zbMATH DE number 4046198