On the stability properties of perturbed linear nonstationary systems
type: Item
instance of: scholarly article
title: On the stability properties of perturbed linear nonstationary systems
zbMATH Open document ID: 0533.34040
DOI: 10.1016/0022-247X(82)90190-1
author: A. Vannelli
author: M. Vidyasagar
author: Abraham Boyarsky
published in: Journal of Mathematical Analysis and Applications
publication date: 1982-01-01T00:00:00Z
review text: The authors discuss the stability properties of perturbed linear nonstationary systems \(\dot x(t)=(A(t)+B(t))x(t)\) with respect to those of the unperturbed linear nonstationary system \(\dot x(t)=A(t)x(t).\) Further, the stability properties of discrete perturbed systems \(x_{k+1}=(A_ k+B_ k)x_ k\) and discrete unperturbed systems \(x_{k+1}=A_ kx_ k\) are investigated. The concepts of stability, asymptotic stability and exponential or geometrical stability are applied. Four theorems are presented and proven for continuous systems. It is found, for example, that the perturbed system is asymptotically stable if the unperturbed system is exponentially stable, A(t) is bounded and B(t)\(\to 0\) as \(t\to \infty\). Six more theorems are found for discrete systems which lead to the following final result: Under some assumptions on \(B_ k\), the perturbed discrete system is geometrically stable iff the corresponding unperturbed system is geometrically stable.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 3846011
zbMATH Keywords: exponential stability
zbMATH Keywords: perturbed linear nonstationary systems
zbMATH Keywords: asymptotic stability
zbMATH Keywords: geometrical stability
MaRDI profile type: Publication
cites work: Q3256529
cites work: Q4093255
cites work: Q5584086
cites work: Q5580482
cites work: &lt;tex&gt;L_{p}&lt;/tex&gt;stability of time-varying linear feedback systems
cites work: &lt;tex&gt;L_infty&lt;/tex&gt;-stability criteria for interconnected systems using exponential weighting
full work available at URL: 0022-247x(82)90190-1
OpenAlex ID: W2030850916
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description: scientific article; zbMATH DE number 3846011