Fractional hold circuits versus positive realness of discrete transfer functions

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.