The method of Lyapunov functions for systems of linear difference equations with almost periodic coefficients
type: Item
instance of: scholarly article
title: The method of Lyapunov functions for systems of linear difference equations with almost periodic coefficients
zbMATH Open document ID: 0873.39006
DOI: 10.1007/BF02104765
author: O. V. Kirichenova
author: A. S. Kotyurgina
author: R. K. Romanovskii
published in: Siberian Mathematical Journal
publication date: 1997-07-24T00:00:00Z
review text: In their article [Mat. Zametki 52, No. 6, 10-14 (1992; Zbl 0798.34056)], \textit{S. M. Dobrovol'skij}, \textit{A. S. Kotyurgina} and \textit{R. K. Romanovskij} established a test exponential stability of the system \(\dot x=A(t)x\) in terms of the Lyapunov function \(V=\langle G(t)x,x\rangle\) with almost periodic \(A(t)\) and \(G(t)\). It was shown that for the indicated class the condition on the derivative \(\overset\circ V\) can be essentially weakened in comparison with Lyapunov's theorem for general linear systems. In the present article, we obtain a difference analog of the result.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1023988
zbMATH Keywords: systems of linear difference equations
zbMATH Keywords: almost periodic coefficients
zbMATH Keywords: test exponential stability
zbMATH Keywords: Lyapunov function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1023988