On Canonical Realizations with Unbounded Infinitesimal Generators
Conference : 11th Annual Allerton Conference on Circuit and System Theory pp. 1-10
Date: October 03 - October 05, 1973
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 Co -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.