Stability of differential-algebraic equations under uncertainty
type: Item
instance of: scholarly article
title: Stability of differential-algebraic equations under uncertainty
zbMATH Open document ID: 1416.34005
DOI: 10.1134/S0012266118070030
published in: Differential Equations
publication date: 2018-10-23T00:00:00Z
review text: In this paper, the authors consider the robust stability of a linear constant-coefficient differential-algebraic equation (DAE) \[ Ax'(t)+Bx(t)=0,\quad t\geq 0, \tag{1} \] where $A$ and $B$ are given real $n\times n$ matrices and $x(t)$ is the unknown $n$-dimensional function. Here, it is assumed that $\mathrm{det}A=0$. First, the structure of DAE (1) is characterized by the notion of unsolvability index. Then, the authors consider perturbed systems \[ (A+\Theta _1)x'(t)+(B+\Theta _2)x(t)=0,\quad t\geq 0, \tag{2} \] and investigate the robust stability of DAE (1) under perturbations. The authors define a special class of structured perturbations which does not change the internal structure of DAE (1). Then, under perturbations belonging to this class, the real stability radius of DAE (1) is defined, which is actually the stability radius of the underlying ODE of (1). Finally, as a simple consequence of the corresponding result for ODEs, a formula of the stability radius is obtained.
reviewed by: Vu Hoang Linh
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6962874
zbMATH Keywords: linear differential-algebraic equation
zbMATH Keywords: unsolvability index
zbMATH Keywords: perturbation
zbMATH Keywords: asymptotic stability
zbMATH Keywords: stability radius
author: Alla Arkad'evna Shcheglova
author: Alekseĭ Denisovich Kononov
MaRDI profile type: Publication
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full work available at URL: s0012266118070030
OpenAlex ID: W2886514889
Wikidata QID: Q129376238
description: scientific article; zbMATH DE number 6962874