Voir la notice de l'article provenant de la source Numdam
In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes and, in particular, exponential stability of heat exchangers. Through concrete examples we show how Lyapunov’s second method may be extended to stability analysis of nonlinear hyperbolic PDE. Meanwhile we explain how the method is adapted to the framework of Banach spaces , .
@article{COCV_2009__15_2_403_0,
author = {Tchousso, Abdoua and Besson, Thibaut and Xu, Cheng-Zhong},
title = {Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using {Lyapunov's} second method},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {403--425},
publisher = {EDP-Sciences},
volume = {15},
number = {2},
year = {2009},
doi = {10.1051/cocv:2008033},
mrnumber = {2513092},
zbl = {1167.37036},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008033/}
}
TY - JOUR AU - Tchousso, Abdoua AU - Besson, Thibaut AU - Xu, Cheng-Zhong TI - Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 403 EP - 425 VL - 15 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008033/ DO - 10.1051/cocv:2008033 LA - en ID - COCV_2009__15_2_403_0 ER -
%0 Journal Article %A Tchousso, Abdoua %A Besson, Thibaut %A Xu, Cheng-Zhong %T Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 403-425 %V 15 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008033/ %R 10.1051/cocv:2008033 %G en %F COCV_2009__15_2_403_0
Tchousso, Abdoua; Besson, Thibaut; Xu, Cheng-Zhong. Exponential stability of distributed parameter systems governed by symmetric hyperbolic partial differential equations using Lyapunov's second method. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 2, pp. 403-425. doi: 10.1051/cocv:2008033
Cité par Sources :