Stability issues in regular and noncritical singular DAEs
type: Item
instance of: scholarly article
title: Stability issues in regular and noncritical singular DAEs
zbMATH Open document ID: 1042.34005
DOI: 10.1023/A:1019711532679
author: Ricardo Riaza
published in: Acta Applicandae Mathematicae
publication date: 2003-03-11T00:00:00Z
review text: The author surveys results on the stability of equilibria in both regular and singular differential algebraic equations. After a brief review of some basic notions concerning differential-algebraic equations including singularity induced bifurcations, he discusses the regular case: first, linear systems are studied using matrix pencils, then the theory is extended to semiexplicit and quasilinear systems. In the treatment of singular equations, the author distinguishes between stationary and nonstationary problems. In the latter case, he analyses index 0 and index 1 equations. The main point is to prove the existence of a submanifold, transversal to the singular locus, on which the dynamics is well-defined. Finally, the stationary case is studied for index 0 equations. Again, matrix pencils are the basic tools, although new complications arise since the relevant pencils are singular.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 1879597
zbMATH Keywords: differential-algebraic equation
zbMATH Keywords: stability
zbMATH Keywords: singularity
zbMATH Keywords: bifurcation
zbMATH Keywords: matrix pencil
zbMATH Keywords: linearisation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1879597