Stabilization of distributed control systems with delay

In this paper the asymptotic stabilization of linear distributed parameter control systems with delay is considered. Specifically, we are concerned with the class of control systems described by the equation x′(t)=Ax(t)+L(xt)+Bu(t)x′(t)=Ax(t)+L(xt)+Bu(t), where AA is the infinitesimal generator of a strongly continuous semigroup on a Banach space XX. Assuming appropriate conditions, we will show that the usual spectral controllability assumption implies the feedback stabilization of the system. Applications to systems described by partial differential equations with delay are given.