具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

Exponential Stabilization of Nonuniform Timoshenko Beamwith a Locally Distributed Feedback and a Boundary One

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.

The stabilization problem of a nonuniform Timoshenko beam system with a locally distributed feedback control and a boundary one is studied. First, based on the published criterion for the asymptotic stability of the related distributed system, we prove the asymptotic stability of the energy corresponding to the closed loop system with only one distributed feedback control. Then, by virtue of frequency domain multiplier method, we prove that the closed loop system with both a locally distributed feedback control and a boundary one is of exponential decay.