On uniform exponential stability of semi-discrete scheme for 1-D wave equation with a tip mass

被引：0
|
作者：
Zhao X. [1 ]
Guo B.-Z. [1 ]
机构：
[1] School of Mathematics and Physics, North China Electrical Power University, Beijing
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2024年 / 41卷 / 05期
基金：
中国国家自然科学基金;
关键词：
finite difference method; tip mass; uniform exponential stability; wave equations;
D O I：
10.7641/CTA.2023.21002
中图分类号：
学科分类号：
摘要：
Most of the infinite-dimensional systems are described by partial differential equations (PDEs). For PDEs, discretization is most often necessarily for numerical simulation and applications. This paper considers the uniform exponential stability of a semi-discrete model for a 1-D wave equation with tip mass under boundary feedback control. The original closed-loop system is transformed firstly into a low-order equivalent system by order reduction method and the exponential stability of the transformed system by an indirect Lyapunov method is established. The equivalent system is then discretized into a series of semi-discrete systems in spacial variable. Parallel to the continuous system, the semi-discrete systems are proved to be uniformly exponentially stable by means of the indirect Lyapunov method. Numerical simulations illustrate why the classical semi-discrete scheme does not preserve the uniformly exponential stability while the order reduction semi-discrete scheme does. © 2024 South China University of Technology. All rights reserved.
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页码：950 / 956
页数：6
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