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

Abstract

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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.

How to cite

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Matignon, 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 -

References

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