Abstract
This paper studies approximate realizations of pseudo-rational impulse responses and discusses the related convergence problems Introducing a subclass S of pseudo-rational impulse responses, we prove that various delay-differential systems are included in this class: systems of retarded type, neutral type and infinitedelay systems.
Since pseudo-rational impulse responses can be represented in terms of distributions, one can discretize them by replacing some distributions with suitable linear combinations of Dirac δ-distributions and derive the approximate impulse responses. The resulting approximate impulse responses are shown to admit finitedimensional realizations and these realizations are given in the observable canonical form by the aid of the dual form of Fuhrmann realizations, in relation to the topologically observable realizations of pseudo-rational impulse responses. Estimation of approximation rate, as well as the proof of convergence, of the approximate models is given. A neutral delay-differential system is presented as an example along with some numerical results in the final section.
