The Riesz basis property of discrete operators and application to a Euler-Bernoulli beam equation with boundary linear feedback control

We give an abstract condition for Riesz basis generation for discrete operators in Hilbert space, from which we show that the generalized eigenfunctions of a Euler-Bernoulli beam equation with boundary linear feedback control form a Riesz basis for the state Hilbert space. As a consequence, the asymptotic expression of eigenvalues as well as exponential stability are readily presented.