On structured perturbations for two classes of linear infinite-dimensional systems

This paper considers two classes of infinite-dimensional systems described by an abstract differential equation x overdot(t) = (A + B Delta C)x(t), x(0) = x(0), on a Hilbert space, where A, B, C are linear, possibly unbounded operators and Delta is an unknown, linear, bounded perturbation. The two classes of systems are defined in terms of properties imposed on the triple {A, B, C}. It is proved that for every Delta the perturbed system {A + E Delta F, B, C} inherits all the properties of the unperturbed system {A, B, C} if {A, E, F} and {A, B, C} are in the same class.