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.
Keywords: asymptotic stability, well-posed systems, Lyapunov functional, diffusive representation, fractional calculus
@article{COCV_2005__11_3_487_0,
author = {Matignon, Denis and Prieur, Christophe},
title = {Asymptotic stability of linear conservative systems when coupled with diffusive systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {487--507},
year = {2005},
publisher = {EDP Sciences},
volume = {11},
number = {3},
doi = {10.1051/cocv:2005016},
mrnumber = {2148855},
zbl = {1125.93030},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2005016/}
}
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 PY - 2005 SP - 487 EP - 507 VL - 11 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2005016/ DO - 10.1051/cocv:2005016 LA - en ID - COCV_2005__11_3_487_0 ER -
%0 Journal Article %A Matignon, Denis %A Prieur, Christophe %T Asymptotic stability of linear conservative systems when coupled with diffusive systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2005 %P 487-507 %V 11 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2005016/ %R 10.1051/cocv:2005016 %G en %F COCV_2005__11_3_487_0
Matignon, Denis; Prieur, Christophe. Asymptotic stability of linear conservative systems when coupled with diffusive systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 487-507. doi: 10.1051/cocv:2005016
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