控制理论与应用2024，Vol.41Issue(5)：950-956,7.DOI:10.7641/CTA.2023.21002
具有端点质量的一维波动方程半离散格式的一致指数稳定性
On uniform exponential stability of semi-discrete scheme for 1-D wave equation with a tip mass
摘要
Abstract
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 ex-ponential 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 ex-ponential 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 simula-tions illustrate why the classical semi-discrete scheme does not preserve the uniformly exponential stability while the order reduction semi-discrete scheme does.关键词
波动方程/端点质量/有限差分方法/一致指数稳定Key words
wave equations/tip mass/finite difference method/uniform exponential stability引用本文复制引用
赵希,郭宝珠..具有端点质量的一维波动方程半离散格式的一致指数稳定性[J].控制理论与应用,2024,41(5):950-956,7.基金项目
国家自然科学基金项目(12131008)资助.Supported by the National Natural Science Foundation of China(12131008). （12131008）
