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		Junmin WANG,Baozhu GUO,Kunyi YANG.[en_title][J].Control Theory and Technology,2008,6(4):341~350.[Copy]

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JunminWANG，BaozhuGUO,KunyiYANG
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Received:September 17, 2007Revised:January 30, 2008

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Stability analysis for an Euler-Bernoulli beam under local internal control and boundary observation

Junmin WANG， Baozhu GUO, Kunyi YANG

(Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China; Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100080, China)

Abstract:

An Euler-Bernoulli beam system under the local internal distributed control and boundary point observation is studied. An infinite-dimensional observer for the open-loop system is designed. The closed-loop system that is nondissipative is obtained by the estimated state feedback. By a detailed spectral analysis, it is shown that there is a set of generalized eigenfunctions, which forms a Riesz basis for the state space. Consequently, both the spectrum-determined growth condition and exponential stability are concluded.

Key words: Euler-Bernoulli equation Observer Riesz basis Controllability and observability Stability