摘要
该文考虑一端固定 ,一端具负荷的梁的振动问题 .证明了线性反馈的闭环系统是一个 Riesz谱系统 ,即系统存在一列广义本征函数列构成状态空间的 Riesz基 .从而系统的谱确定增长条件成立 .在此过程中 ,简单的导出了系统本征值的渐近展开式 .
An Euler Bernoulli beam equation with one end fixed and a tip mass at another end is considered.It is shown that the closed loop system under boundary linear feedback control is a riesz spectral system.That is,there is a sequence of generalized eigenfunctions,which forms a riest basis for the state Hilberf space.The spectrum-determined growth condition is hence established.In the meanwhile,the asymptotic expansion of the eigenvolues is derived and the exponential seability of the system is concluded.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2000年第4期568-576,共9页
Acta Mathematica Scientia
基金
国家自然科学基金项目!(批准号 :69874 0 0 3)资助