Realization of Pseudo-Rational Input/Output Maps and Its Spectral Properties

Abstract

Realization of a special class of input/output maps is considered. A linear input/output map which belongs to this class is called pseudo-rational, and it behaves in a way similar to the input/output maps of finite-dimensional systems in the following sense : To determine the canonical state space, only the output data on a bounded time interval is needed. Central examples of this class of input/output maps are those of delay-differential systems. A concrete representation for the canonical space is given ; and then it is used to give an explicit differential equation description. Some spectral properties which are very similar to those of the delay-differential systems are also proved. Some examples are demonstrated to illustrate the realization procedure.