This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L$$ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.
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DOI : 10.1051/cocv/2019069
Mots-clés : Diagonal semilinear hyperbolic systems, saturation, Lyapunov theory
@article{COCV_2020__26_1_A23_0,
author = {Dus, Mathias and Ferrante, Francesco and Prieur, Christophe},
title = {On {\protect\emph{L}\protect\textsuperscript{\ensuremath{\infty}}} stabilization of diagonal semilinear hyperbolic systems by saturated boundary control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019069},
mrnumber = {4070783},
zbl = {1441.93241},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019069/}
}
TY - JOUR AU - Dus, Mathias AU - Ferrante, Francesco AU - Prieur, Christophe TI - On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019069/ DO - 10.1051/cocv/2019069 LA - en ID - COCV_2020__26_1_A23_0 ER -
%0 Journal Article %A Dus, Mathias %A Ferrante, Francesco %A Prieur, Christophe %T On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019069/ %R 10.1051/cocv/2019069 %G en %F COCV_2020__26_1_A23_0
Dus, Mathias; Ferrante, Francesco; Prieur, Christophe. On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 23. doi : 10.1051/cocv/2019069. http://www.numdam.org/articles/10.1051/cocv/2019069/
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Cité par Sources :
Research by F. Ferrante has been partially supported by the CNRS-INS2I under the JCJC grant CoBrA and by the Grenoble Institute of Technology under the grant CrYStAL.
