On null controllability of linear systems via bounded control functions

This paper considers the problem of exact null controllability of infinite dimensional linear systems in non-reflexive state spaces and reflexive control spaces. The starting point of this paper is the work of A. Vieru (Systems & Control Lett. 54 (2005) 331-337), which obtains the characterization of exact null controllability via bounded control functions in reflexive state spaces and control spaces (see Remark 2.2 of (Systems & Control Lett. 54 (2005) 331-337)). We will show here if the state space X is a general Banach space and U is reflexive, the similar result is also valid for exact null controllability via bounded control functions, which extends the results of (Systems & Control Lett. 54 (2005) 331-337)