Stability of linear differential-algebraic systems
type: Item
instance of: scholarly article
title: Stability of linear differential-algebraic systems
zbMATH Open document ID: 1081.34006
published in: Differential Equations
publication date: 2005-05-23T00:00:00Z
review text: Linear differential-algebraic equations (DAEs) \[ A(t)x'(t)+B(t)x(t)=f(t) \] are addressed in this paper using left-regularizing operators. The authors remark that for sufficiently smooth coefficients \(A\) and \(B\), the existence of such a left-regularizing operator is equivalent to the existence of a Cauchy-type general solution and for analytic cases, to the existence of a standard canonical form. Within this framework, they obtain Lyapunov stability criteria and prove an analog of Floquet's theorem leading to stability results for periodic homogeneous DAEs.
reviewed by: Ricardo Riaza
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 2170209
zbMATH Keywords: linear differential-algebraic equations
zbMATH Keywords: regularization
zbMATH Keywords: Lyapunov stability
author: Alla Arkad'evna Shcheglova
author: V. F. Chistyakov
MaRDI profile type: Publication
full work available at URL: b:dieq.0000028713.18251.ea
OpenAlex ID: W2048834597
DOI: 10.1023/B:DIEQ.0000028713.18251.EA
description: scientific article; zbMATH DE number 2170209