Fractional hold circuits versus positive realness of discrete transfer functions

The appropriate use of fractional-order holds (β-FROH) ofcorrecting gains β∈[−1,1] as an alternative to theclassical zero-and first-order holds (ZOHs, FOHs) is discussedrelated to the positive realness of the associate discretetransfer functions obtained from a given continuous transferfunction. It is proved that the minimum direct input/output gain(i.e., the quotient of the leading coefficients of the numeratorand denominator of the transfer function) needed for discretepositive realness may be reduced by the choice of β comparedto that required for discretization via ZOH