Fractional hold circuits versus positive realness of discrete transfer functions

Abstract

The appropriate use of fractional-order holds(beta-FROH) of correcting gains beta is an element of[- 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 beta compared to that required for discretization via ZOH.