Some remarks on reachability of infinite-dimensional linear systems

In this paper we shall be concerned with the question of reachability when allowing distribution inputs. We show that a certain class of systems accept distribution inputs, but, in general, they cannot be exactly reachable. We shall also consider the problem of the uniqueness of canonical realizations in relation to exact reachability, and show that Matsuo's result on uniqueness (Ph.D. dissertation, in preparation) does not apply to the example given in Baras, Brockett, and Fuhrmann IEEE Trans. Automatic ControlAC-19 (1974), 693–700].