Riesz Basis Generation of a Hybrid System with Boundary Feedback Control

Abstract

In this paper, an Euler-Bernoulli equation with one end fixed and a tip mass at another end is considered. By using Guo's conclusion that the Riesz basis property holds for the general system if its associated characteristic equation is strongly regular, it is shown that the Riesz basis property can be established for the closed-loop system under boundary linear feedback control. In the meanwhile, we get the conclusions that the system operator A generates a C 0 -semigroup eAt on state space and the spectrum-determined growth condition holds: s(A) = w(A).