Riesz basis property of a hybrid system by boundary feedback control

Abstract

The purpose of this work is to study the Riesz basis generation of the well-known SCOLE model. 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 a beam equation with an endmass. Furthermore, we get the conclusions that the system operator A generates a C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> -semigroup ℯ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">At</sup> on state space and the spectrum-determined growth condition holds : s(A) = ω(A).