Conditions on feedback stabilization of systems with state and input delays in banach spaces

Semigroup approach to feedback stabilization of systems with state delay has already been introduced in the literature. The aim of this work is to apply the semigroup approach to the feedback stabilization of partial differential systems with state and input delays. Here we shall work with general state Banach spaces and a general class of state and delay operators. We use a generalization of Hautus criteria to derive a necessary condition for the stabilization of the delay system. We show that this condition is only sufficient if the differential operator of the delay free system generates a compact semigroup and the control space has a finite dimension.