具有一般耗散边界反馈的Euler-Bernoulli梁的指数镇定问题(英文)

Exponential Stabilization of Euler-Bernoulli Beam with Dissipative Boundary Feedback

讨论具有一般线性耗散边界反馈的Eulel-Bernoulli梁的指数镇定问题.首先将所讨论的系统化为抽象空间中的发展方程,并利用Co半群理论给出闭环系统解的存在唯一性.其次,对相应的闭环系统特征方程进行详尽的讨论计算,得到了系统本征值的分布特性,从而利用Lassel不变原理得到了闭环系统渐近稳定的充分必要条件.最后通过对闭环系统的本征值及其相应的本征函数进行估计,导出了相应的闭环系统指数稳定的充分必要条件.

This paper studies the stabilization problem of Euler-Bernoulli beam with general dissi-pative boundary feedback controls. First, by virtue of semigroup theory, the considered system is converted into an evolution equation in abstract space and the uniqueness of the solution to the evolution equation is proved. Then the eigenvalues of the closed loop system is studied and the necessary and sufficient condition for the closed loop system to be asymptotically stable is derived. Finally, the condition for the closed loop system to be exponentially stable is worked out by esti-mating the corresponding eigenfunctions.