关键词: 分布参数, Riesz基, 谱确定增长条件, 稳定性

Abstract:

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.

Key words: Distributed system, Riesz basis, Beam equation, Stability