Fractional hold circuits for the design of positive realness discrete transfer functions

The appropriate use of fractional order holds (beta - FROH) of correcting gains beta isin [-1,1 ] as an alternative to the classical zero and first order-holds (respectively, 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 beta compared to that required for discretization via a ZOH