# Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks*

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 2, page 552-574
- ISSN: 1292-8119

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topHan, Zhong-Jie, and Xu, Gen-Qi. "Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks*." ESAIM: Control, Optimisation and Calculus of Variations 17.2 (2011): 552-574. <http://eudml.org/doc/276334>.

@article{Han2011,

abstract = {
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.
},

author = {Han, Zhong-Jie, Xu, Gen-Qi},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Timoshenko beam; exponential stability; time delay; Riesz basis; feedback control},

language = {eng},

month = {5},

number = {2},

pages = {552-574},

publisher = {EDP Sciences},

title = {Exponential stability of Timoshenko beam system with delay terms in boundary feedbacks*},

url = {http://eudml.org/doc/276334},

volume = {17},

year = {2011},

}

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

DA - 2011/5//

PB - EDP Sciences

VL - 17

IS - 2

SP - 552

EP - 574

AB -
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.

LA - eng

KW - Timoshenko beam; exponential stability; time delay; Riesz basis; feedback control

UR - http://eudml.org/doc/276334

ER -

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