On Canonical Realizations with Unbounded Infinitesimal Generators

In this paper, we study canonical (controllable and observable) realiza­tions for infinite dimensional linear systems. In these realizations the infinitesimal state transition operator is unbounded but the generator of a C_o -semigroup in a Hilbert space. We present ways to reduce a realization to a canonical one. We also study the relation between the analytic proper­ties of a transfer function and the spectral properties of the infinitesimal generators in its realizations. Finally, we describe a class of transfer functions which can be realized by a system with an infinitesimal generator having spectral properties closely related to the singularities of the trans­fer functions.