Lower bounds in rational approximation to delays
Laurent Baratchart  1@  
1 : APICS (Inria Sophia Antipolis - Méditerranée)  (CRISAM)  -  Site web
Institut National de Recherche en Informatique et en Automatique
2004 route des Lucioles BP 93 06902 Sophia Antipolis -  France

Transfer functions of delay systems are hard to approximate by rational functions. This phenomenon, which is interesting
from the point of view of approximation theory, is also a concern in problems where the frequency response of a device must be approximated by a model
involving rational elements; for instance in identification and matching. In this talk, we derive a lower bound for the sup-norm approximation to a pure delay exp(-sT) (T the delay, s the complex variable) by a rational function of given degree on a finite interval of the imaginary axis, under a norm constraint on the error at all other points of the imaginary axis.

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