Despite of the fact that distributed (internal) controls are usually used to obtain controllability for a hyperbolic system with vanishing characteristic speeds, this paper is, however, devoted to study the case where only boundary controls are considered. We first prove that the system is not (null) controllable in finite time. Next, we give a sufficient and necessary condition for the asymptotic stabilization of the system under a natural feedback.

DOI: 10.1051/cocv/2015031

Keywords: Hyperbolic systems, controllability, stabilization, vanishing characteristic speed, zero eigenvalue

^{1, 2, 3}; Wang, Zhiqiang

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@article{COCV_2016__22_1_134_0, author = {Hu, Long and Wang, Zhiqiang}, title = {On boundary control of a hyperbolic system with a vanishing characteristic speed}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {134--147}, publisher = {EDP-Sciences}, volume = {22}, number = {1}, year = {2016}, doi = {10.1051/cocv/2015031}, zbl = {1336.93031}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2015031/} }

TY - JOUR AU - Hu, Long AU - Wang, Zhiqiang TI - On boundary control of a hyperbolic system with a vanishing characteristic speed JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 134 EP - 147 VL - 22 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2015031/ DO - 10.1051/cocv/2015031 LA - en ID - COCV_2016__22_1_134_0 ER -

%0 Journal Article %A Hu, Long %A Wang, Zhiqiang %T On boundary control of a hyperbolic system with a vanishing characteristic speed %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 134-147 %V 22 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2015031/ %R 10.1051/cocv/2015031 %G en %F COCV_2016__22_1_134_0

Hu, Long; Wang, Zhiqiang. On boundary control of a hyperbolic system with a vanishing characteristic speed. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 1, pp. 134-147. doi : 10.1051/cocv/2015031. http://www.numdam.org/articles/10.1051/cocv/2015031/

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