On the Unboundedness of Control Operators for Bilinear Systems

Abstract

The aim of this work is to study the classes of unbounded linear control operators which ensure the existence and uniqueness of the mild and strong solutions of certain bilinear control systems. By an abstract approach, similar to that adopted by Weiss [18], we obtain a connection between these classes and those constituted by control operators with values in the extrapolation space associated to the state space. We show the localization of these classes and, in certain cases, the identification with concrete spaces.