# Asymptotic stability of linear conservative systems when coupled with diffusive systems

Denis Matignon; Christophe Prieur

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 3, page 487-507
- ISSN: 1292-8119

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topMatignon, Denis, and Prieur, Christophe. "Asymptotic stability of linear conservative systems when coupled with diffusive systems." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2010): 487-507. <http://eudml.org/doc/90774>.

@article{Matignon2010,

abstract = { In this paper we study linear conservative systems of finite
dimension
coupled with an infinite dimensional system of diffusive type.
Computing the time-derivative of an
appropriate energy functional along the solutions helps us to
prove the well-posedness of the system
and a stability property.
But in order to prove asymptotic stability we need to apply
a sufficient spectral condition. We also illustrate the sharpness of this
condition by exhibiting some systems for which we do not have the asymptotic
property.
},

author = {Matignon, Denis, Prieur, Christophe},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Asymptotic stability; well-posed systems; Lyapunov functional;
diffusive representation; fractional calculus.; diffusive representation; fractional calculus},

language = {eng},

month = {3},

number = {3},

pages = {487-507},

publisher = {EDP Sciences},

title = {Asymptotic stability of linear conservative systems when coupled with diffusive systems},

url = {http://eudml.org/doc/90774},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Matignon, Denis

AU - Prieur, Christophe

TI - Asymptotic stability of linear conservative systems when coupled with diffusive systems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 3

SP - 487

EP - 507

AB - In this paper we study linear conservative systems of finite
dimension
coupled with an infinite dimensional system of diffusive type.
Computing the time-derivative of an
appropriate energy functional along the solutions helps us to
prove the well-posedness of the system
and a stability property.
But in order to prove asymptotic stability we need to apply
a sufficient spectral condition. We also illustrate the sharpness of this
condition by exhibiting some systems for which we do not have the asymptotic
property.

LA - eng

KW - Asymptotic stability; well-posed systems; Lyapunov functional;
diffusive representation; fractional calculus.; diffusive representation; fractional calculus

UR - http://eudml.org/doc/90774

ER -

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