带有内部扰动的Timoshenko梁系统的指数稳定性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 185-198.

带有内部扰动的Timoshenko梁系统的指数稳定性

张丽萍¹, 刘东毅², 张国山¹

1. 天津大学电气与自动化工学院天津 300072;
2. 天津大学理学院天津 300072

收稿日期:2016-03-28 修回日期:2016-09-13 出版日期:2017-02-26 发布日期:2017-02-26
作者简介:张丽萍,E-mail:lipingzhang@tju.edu.cn;刘东毅,E-mail:dyliu@tju.edu.cn;张国山,E-mail:zhanggs@tju.edu.cn
基金资助:
国家自然科学基金（61573252）

Exponential Stabilization of a Timoshenko Beam System with Internal Disturbances

Zhang Liping¹, Liu Dongyi², Zhang Guoshan¹

1. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072;
2. Department of Mathematics, Tianjin University, Tianjin 300072

Received:2016-03-28 Revised:2016-09-13 Online:2017-02-26 Published:2017-02-26
Supported by:
Supported by the NSFC (61573252)

摘要/Abstract

摘要：

该文考虑了带有内部扰动的Timoshenko梁的稳定性问题.根据滑模控制的思想，设计非线性分布反馈控制器来降低额外扰动的影响.由于所导出的受控系统是非线性系统，应用非线性极大单调算子理论和变分原理分析非线性闭环系统的可解性.并且通过Lyapunov方法证明闭环系统的指数稳定性.

关键词: 指数稳定性, Timoshenko梁, 极大单调算子, 内部扰动, 非线性分布反馈控制

Abstract:

In this paper, we consider the stabilization of a Timoshenko beam with interior disturbances. On the basis of the idea of sliding-mode control, we design nonlinear distributed feedback controllers to reduce the effects of the external disturbances. Due to the resulting controlled system is a nonlinear system, the theories of nonlinear maximal monotone operators and variation principle are employed for the solvability analysis of the nonlinear closed-loop system. Moreover we show that exponential stability of the closed-loop system by the Lyapunov method.

Key words: Exponential stability, Timoshenko beam, Maximal monotone operator, Internal disturbance, Nonlinear distributed feedback controller

中图分类号:

O231.9

张丽萍, 刘东毅, 张国山. 带有内部扰动的Timoshenko梁系统的指数稳定性[J]. 数学物理学报, 2017, 37(1): 185-198.

Zhang Liping, Liu Dongyi, Zhang Guoshan. Exponential Stabilization of a Timoshenko Beam System with Internal Disturbances[J]. Acta mathematica scientia,Series A, 2017, 37(1): 185-198.

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