Institute of Systems Science Academy of Mathematics and System Sciences Academia Sinica Beijing 100081 — China | Department of Mathematics
The University of Kong Kong — Hong Kong |
ABSTRACT
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-Bernouilli 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.
2000 Mathematics Subject Classification: 35P20, 93D15.