On data-dependence of exponential stability and stability radii for linear time-varying differential-algebraic systems
type: Item
instance of: scholarly article
title: On data-dependence of exponential stability and stability radii for linear time-varying differential-algebraic systems
zbMATH Open document ID: 1162.34004
author: Nguyen Huu Du
author: Vu Hoang Linh
author: Chuan J. Chyan
published in: Journal of Differential Equations
publication date: 2008-10-21T00:00:00Z
review text: The authors consider time-varying linear implicit differential equations \[ E(t)\dot{x}(t)=A(t)x(t),\quad t\geq 0, \] which are strongly index one, i.e.\ the equation can be decoupled into an explicite differential equation and an algebraic equation, furthermore, certain transformation matrices are assumed to be bounded. For this class of equations the stability radius with respect to structured dynamic perturbations of the matrix \(A\) and the Bohl exponent are defined and studied. It follows that the zero solution of the above equation is exponentially stable if, and only if, the Bohl exponent is negative and it is shown that exponential stability is equivalent to the property that the inhomogeneous equation \[ E(t)\dot{x}(t)=A(t)x(t)+f(t),\quad t\geq 0, \] has a ``bounded-input-bounded-output'' property. Finally, the dependency of the stability radius and of the Bohl exponent on additive changes in the matrix \(A\) are studied. The authors obtain ``continuity''-results, i.e.\ sufficiently small disturbances in the matrix \(A\) will not change the stability radius and the Bohl exponent significantly.
reviewed by: Stephan Trenn
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 5354957
zbMATH Keywords: exponential stability
zbMATH Keywords: Bohl exponent
zbMATH Keywords: stability radii
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: data-dependence
MaRDI profile type: Publication
full work available at URL: j.jde.2008.07.016
OpenAlex ID: W2009452741
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DOI: 10.1016/J.JDE.2008.07.016
description: scientific article; zbMATH DE number 5354957