EXPONENTIAL STABILITY OF STRING SYSTEM WITH VARIABLE COEFFICIENTS UNDER NON-COLLOCATED FEEDBACK CONTROLS

被引：9

作者：

Chen, Yunlan ^{[1
]}

Han, Zhongjie ^{[1
]}

Xu, Genqi ^{[1
]}

Liu, Dongyi ^{[1
]}

机构：

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

来源：

ASIAN JOURNAL OF CONTROL | 2011年 / 13卷 / 01期

关键词：

Variable coefficient string system; non-collocated feedback control; eigenvalue; Riesz basis; exponential stability; RIESZ BASIS PROPERTY; BOUNDARY FEEDBACK; TIMOSHENKO BEAM; STABILIZATION;

D O I：

10.1002/asjc.255

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, we describe a linear boundary non-collocated feedback controller to stabilize a string system with variable coefficients and investigate the exponential stability of the closed-loop system. We show that the system associates with a C-0 semigroup. Through the asymptotic analysis technique, we get the asymptotic values of all eigenvalues of the system operator A. Furthermore, we prove that there is a sequence of generalized eigenvectors of A that forms a Riesz basis with parentheses for the energy state space. Hence, the system satisfies the spectrum determined growth assumption. Finally, we show that the system is exponentially stable with suitable choice of the feedback gains.

引用

页码：148 / 163

页数：16

共 24 条

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