On spectrum and Riesz basis assignment of infinite dimensional linear systems by bounded linear feedbacks

摘要

In this paper, we consider the following linear system of single input on a separable Hilbert space H: /spl phi//spl dot/(t)=A/spl phi/(t)+bu(t), where the operator A is the generator of a C/sub 0/-semigroup on R and the vector b is not necessarily in H (for the case of boundary controls). We assume that the operator A has compact resolvents, the spectrum of A is discrete and simple and the eigenvectors of A form a Riesz basis in H. We study the spectrum assignability of the system by bounded linear feedbacks of the form: u(t)=>h,/spl phi/(t)