Stabilization of high eigenfrequencies of a beam equation with generalized viscous damping

被引：4

作者：

Li, SJ ^{[1
]}

Yu, JY

Liang, ZD

Zhu, GT

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

[2] Inst Informat & Control, Beijing 100037, Peoples R China

[3] Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1999年 / 37卷 / 06期

关键词：

generalized viscous damping; eigenfrequencies; feedback control; exponential decay;

D O I：

10.1137/S0363012997322546

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, using the one-dimensional vibrating beam equation with generalized viscous damping as a model of vibration of flexible robot arms, it is shown that for such a system the high eigenmodes decay at a uniform rate. The proof is obtained by perturbation theory of linear operators [Y. H. Luo, Acta Math. Sinica, 32 (1991), pp. 556-563] and asymptotic estimates of eigenvectors based on an earlier work of G. B. Birkhoff and M. H. Stone. Feedback control for this class of system is investigated, and a finite-dimensional controller is presented for an exponentially stable closed-loop system. Our method may be used to study nondissipative systems.

引用

页码：1767 / 1779

页数：13

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