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Asymptotic stability of linear conservative systemswhen coupledwith diffusive systems

Published online by Cambridge University Press:  15 July 2005

Denis Matignon  and
Christophe Prieur
Denis Matignon
Affiliation:
Télécom Paris, dépt TSI & CNRS, UMR 5141, 37-39 rue Dareau, 75 014 Paris, France; matignon@tsi.enst.fr
Christophe Prieur
Affiliation:
LAAS - CNRS, 7 avenue du Colonel Roche 31077 Toulouse, France; prieur@laas.fr
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Abstract

In this paper we study linear conservative systems of finitedimensioncoupled with an infinite dimensional system of diffusive type. Computing the time-derivative of anappropriate energy functional along the solutions helps us toprove the well-posedness of the systemand a stability property.But in order to prove asymptotic stability we need to applya sufficient spectral condition. We also illustrate the sharpness of thiscondition by exhibiting some systems for which we do not have the asymptoticproperty.

Keywords

Asymptotic stabilitywell-posed systemsLyapunov functionaldiffusive representationfractional calculus.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 3 , July 2005 , pp. 487 - 507
Copyright
© EDP Sciences, SMAI, 2005

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