Geodesic
Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 2, pp. 552-574

Voir la notice de l'article provenant de la source Numdam

In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the state Hilbert space. Hence the system satisfies the spectrum determined growth condition. Then we conclude the exponential stability of the system under certain conditions. Finally, we give some simulations to support our results.

DOI : 10.1051/cocv/2010009
Classification : 93D15, 93C20, 49K25, 34H05
Keywords: Timoshenko beam, exponential stability, time delay, Riesz basis, feedback control 
@article{COCV_2011__17_2_552_0,
     author = {Han, Zhong-Jie and Xu, Gen-Qi},
     title = {Exponential stability of {Timoshenko} beam system with delay terms in boundary feedbacks},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {552--574},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {2},
     year = {2011},
     doi = {10.1051/cocv/2010009},
     mrnumber = {2801331},
     zbl = {1251.93106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010009/}
}
TY  - JOUR
AU  - Han, Zhong-Jie
AU  - Xu, Gen-Qi
TI  - Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2011
SP  - 552
EP  - 574
VL  - 17
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010009/
DO  - 10.1051/cocv/2010009
LA  - en
ID  - COCV_2011__17_2_552_0
ER  - 
%0 Journal Article
%A Han, Zhong-Jie
%A Xu, Gen-Qi
%T Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2011
%P 552-574
%V 17
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2010009/
%R 10.1051/cocv/2010009
%G en
%F COCV_2011__17_2_552_0
Han, Zhong-Jie; Xu, Gen-Qi. Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 2, pp. 552-574. doi: 10.1051/cocv/2010009

Cité par Sources :