Riesz basis generation, eigenvalues distribution, and exponential stability for a euler-bernoulli beam with joint feedback control

Using an abstract result on Riesz basis generation for discrete operators in general Hilbert spaces, we show, in this article, that the generalized eigenfunctions of an Euler-Bernoulli beam equation ith oint linear feedback control form a Riesz basis for the tate space. The spectrum-determined growth condition is hence obtained. Meanwhile, the exponential stability as well as the asymptotic expansion of eigenvalues are also readily obtained by a straightforward computation