On Spectrum Distribution of Completely Controllable Linear Systems

Abstract

This paper is concerned with the placement of the spectrum of the closed-loop operator $A + BK$ resulting from use of a linear feedback control law $u = Kx$ in the infinite dimensional linear control system $x' = Ax + Bu$. For a class of systems in Hilbert space with certain assumptions on the spectrum of the operator A, a complete characterization of the achievable spectra is obtained. The proofs are carried out in an operator-theoretic context.