Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 373-378
doi:10.1155/DDNS.2005.373
Fractional hold circuits versus positive
realness of discrete transfer functions
Instituto de Investigación y Desarrollo de Procesos, Facultad de Ciencias, Universidad del País Vasco Leioa (Bizkaia), Apartado 644 de Bilbao, Bilbao 48080, Spain
Received 25 October 2004
Copyright © 2005 M. de la Sen and A. Bilbao-Guillerna. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The appropriate use of fractional-order holds (β-FROH) of
correcting gains β∈[−1,1]
as an alternative to the
classical zero-and first-order holds (ZOHs, FOHs) is discussed
related to the positive realness of the associate discrete
transfer functions obtained from a given continuous transfer
function. It is proved that the minimum direct input/output gain
(i.e., the quotient of the leading coefficients of the numerator
and denominator of the transfer function) needed for discrete
positive realness may be reduced by the choice of β compared
to that required for discretization via ZOH.