On Fractional Hold Devices Versus Positive Realness of Discrete Transfer Functions

The appropriate use of fractional order holds (β-FROH) of correcting gains βε[-1,1] as an alternative to the classical zero and first order -holds (ZOH, FOH) 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.