Resumen de Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler-Bernouilli beam with joint feedback control

Bao-Zhu Guo, K. Y. Chan

• 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 with joint linear feedback control form a Riesz basis for the state 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.