Lyapunov, Bohl and Sacker-Sell spectral intervals for differential-algebraic equations
type: Item
instance of: scholarly article
title: Lyapunov, Bohl and Sacker-Sell spectral intervals for differential-algebraic equations
zbMATH Open document ID: 1165.65050
author: Vu Hoang Linh
author: Volker Mehrmann
published in: Journal of Dynamics and Differential Equations
publication date: 2009-05-04T00:00:00Z
review text: The authors extend some classical spectral concepts (Lyapunov, Bohl, Sacker-Sell) that were introduced for ordinary differential equations (ODE), to general linear differential-algebraic equations (DAE) with variable coefficients of the type \[ E(t)x'=A(t)x+f(t) \] on \(I=[0,\infty)\), where \(E,\, A\in C(I,{\mathbb R}^{n\times n})\) and \(f\in C(I,{\mathbb R}^{n})\). The main topics investigated in the present paper include the relations between the spectral characteristics of DAE systems and ODE systems, as well as the stability of the spectra with respect to perturbations arising in the system data. The paper also includes numerical methods for computing the Lyapunov and the Sacker-Sell (exponential dichotomy) spectral intervals. Some open problems are formulated in the last part of this paper.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 5550493
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: strangeness index
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: Bohl exponent
zbMATH Keywords: Sacker-Sell spectrum
zbMATH Keywords: exponential dichotomy
zbMATH Keywords: spectral interval
zbMATH Keywords: smooth QR factorization
zbMATH Keywords: continuous QR algorithm
zbMATH Keywords: discrete QR algorithm
zbMATH Keywords: kinematic equivalence
zbMATH Keywords: Steklov function
describes a project that uses: RODAS
describes a project that uses: Modelica
describes a project that uses: GELDA
MaRDI profile type: Publication
full work available at URL: s10884-009-9128-7
OpenAlex ID: W2002947564
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Lyapunov, Bohl and Sacker-Sell spectral intervals for differential-algebraic equations (DOI)
DOI: 10.1007/S10884-009-9128-7

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