The aim is to study the boundary controllability of a system modelling the vibrations of a network ofN Euler-Bernoulli beams serially connected by (N − 1) vibrating interior point masses. Using the classical Hilbert Uniqueness Method, the control problem is reduced to the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that one of the sufficient conditions for the observability inequality is that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value. This property called spectral gap holds. It is proved using the exterior matrix method due to W.H. Paulsen. Two more asymptotic estimates involving the eigenfunctions are required for the observability inequality to hold. They are established using an adequate basis.

中文翻译：

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具有内部质量的串联的Euler-Bernoulli梁链的边界可控性

目的是研究一个系统的边界可控性，该系统对由（N）串联的N个Euler-Bernoulli梁网络的振动进行建模。− 1）振动内部点质量。使用经典的希尔伯特唯一性方法，将控制问题简化为可观察性不等式的产生。然后用傅立叶级数表示解决方案，以使可观测性不等式的充分条件之一是，涉及此演化问题的空间算子的两个连续大特征值之间的距离优于最小固定值。这种称为光谱间隙的特性成立。WH Paulsen使用外部矩阵方法对此进行了证明。要保持可观察性不等式，还需要两个涉及特征函数的渐近估计。它们建立在充分的基础上。