On invariance of pp-admissibility of control and observation operators to qq-type of perturbations of generator of C0C0-semigroup

In this paper, it is proved in general setting that pp-admissibilities of control operators and observation operators are invariant to any qq-type of perturbations of generator of C0C0-semigroups on Banach space. Moreover, some relations between the ΛΛ-extensions of observation operators with respect to the original generator and the perturbed generator are also characterized, so that the output can be expressed in the mild sense. As an application, the admissibility as well as the mild expressibility of output of a class of observation systems with time delay in state is deduced.