Riesz basis approach to the control of a hybrid system of elasticity

Abstract

This paper deals with the boundary feedback stabilization of a SCOLE model, namely a flexible beam hinged at one end, and free at the other end where a rigid body is attached. using the Riesz basis approach, it is shown that the closed-loop system is a Riesz spectral system and as consequences, the asymptotic expression of eigenvalues and the expoenential stability are concluded. To verify the theoritical developments, numerical study of the spectrum is performed.