This paper studies the feedback stabilizability of linear abstract control systems with unbounded control operators, whose state operators generate analytic semigroups. Under an almost exponential decay condition that ensures the existence of bounded feedback operators, we establish several equivalent characterizations of stabilizability. Our main tool is an extended-state-space construction in which the control operator becomes admissible, combined with a Hautus-type resolvent (frequency-domain) inequality. As an application, we recover and extend existing results to settings in which the semigroup generated by the state operator is non-compact and the control operator may fail to be admissible.
Ma et al. (Tue,) studied this question.