Controllability of infinite dimensional linear systems with unbounded control operator in Banach spaces

The problem of controllability of infinite dimensional linear systems with unbounded control operator in Banach spaces is considered. First, some properties of dual semigroups with respect to Lebesgue measure is presented. Then, based on the properties, the criteria for controllability is established in general Banach spaces. In addition, the robustness of controllability under more general unbounded perturbations is also considered in reflexive Banach spaces.