Stabilization of nonuniform Euler-Bernoulli beam with locally distributed feedbacks |
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Authors: | Xian-bing Cao Qing-xu Yan |
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Institution: | 1Department of Mathematics, School of Sciences, Beijing Technology and Business University, Beijing 100048, China 2Information Engineering School, China Geosciences University, Beijing 100083, China |
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Abstract: | In this article, we study the stabilization problem of a nonuniform Euler-Bernoulli beam with locally distributed feedbacks.
Firstly, using the semi-group theory, we establish the well-posedness of the associated closed loop system. Then by proving
the uniqueness of the solution of a related ordinary differential equations, we derive the asymptotic stability of the closed
loop system. Finally, by means of the piecewise frequency domain multiplier method, we prove that the corresponding closed
loop system can be exponentially stabilized by only one of the two distributed feedback controls proposed in this paper. |
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Keywords: | nonuniform Euler-Bernoulli beam linear locally distributed feedback control linear semigroup exponential stability piecewise multiplier method |
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