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.

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}, publisher = {EDP-Sciences}, volume = {17}, number = {2}, year = {2011}, pages = {552-574}, doi = {10.1051/cocv/2010009}, zbl = {1251.93106}, mrnumber = {2801331}, language = {en}, url = {http://www.numdam.org/item/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, Volume 17 (2011) no. 2, pp. 552-574. doi : 10.1051/cocv/2010009. http://www.numdam.org/item/COCV_2011__17_2_552_0/

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