# On Canonical Realizations with Unbounded Infinitesimal Generators

## On Canonical Realizations with Unbounded Infinitesimal Generators

Title : On Canonical Realizations with Unbounded Infinitesimal Generators
Authors :
Baras, John S.

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.