Abstract: | Let A be a generator of a strongly continuous semigroup of operators, and assume that C and H are operators such that A + CH generates a strongly continuous semigroup SH(t) on X. Let λ0 be a real number in the resolvent set of A, and let ε −1, 1]. Then there are some fairly unrestrictive conditions under which A+(λ0 − A)CH(λ0 − A)− also generates a strongly continuous semigroup SK(t) on X which has the same exponential growth rate as SH(t). Given an input operator B, we can use this to identify a class of feedback perturbations K such that A + BK generates a strongly continuous semigroup. We can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system. For example, we show that if the control on a cantilever beam in the state space H020, 1] × L20, 1] is a moment force on the free end, then we cannot stabilize the beam with an A−1/2-bounded feedback, but we can find an A−1/4-bounded feedback, for any > 0, which does stabilize the beam. |