Exponential stability of uniform Euler-Bernoulli beams with non-collocated boundary controllers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Chen, Yun Lan¹  Xu, Gen Qi¹ 

[1] Tianjin Univ, Dept Math, Tianjin 300072, Peoples R China

关键词: Euler-Bernoulli beam;    Non-collocated controllers;    Asymptotic analysis;    Riesz basis;    Exponential stability;   

DOI  :  10.1016/j.jmaa.2013.07.048

来源: Elsevier

【 摘 要 】

We study the stability of a robot system composed of two Euler-Bernoulli beams with non-collocated controllers. By the detailed spectral analysis, we prove that the asymptotical spectra of the system are distributed in the complex left-half plane and there is a sequence of the generalized eigenfunctions that forms a Riesz basis in the energy space. Since there exist at most finitely many spectral points of the system in the right half-plane, to obtain the exponential stability, we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half-plane. Hence the Riesz basis property ensures that the system is exponentially stable. Finally we give some simulation for spectra of the system. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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