弹性梁点控制、点测量与指数镇定

Pointwise measure, control and stabilization of elastic beams

运用近年来发展的基理论对弹性梁点测量、点控制做一个系统的处理,得到了用速度线性反馈可实现系统的指数镇定的条件且指数镇定当且仅当系统精确可控,在指数镇定的情况下闭环系统的广义本征函数生成能量空间的Riesz基且谱确定增长条件成立。

The pointwise measure, control and stabilization based on the Riesz basis approach developed recently is studied. The condition for the exponential stability under linear feedback of output of velocity is derived. The system is proved to be exponentially stable if and only if the open loop system is exactly controllable. Under the exponential stability condition, the system is further shown to be Riesz spectral system and the spectrum-determined growth condition is therefore verified.