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Discrete Dynamics in Nature and Society
Volume 2005, Issue 3, Pages 373-378

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.


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.