On the intrinsic limiting zeros as the sampling period tends to zero

It is rigorously proved that the limiting discrete zeros located at z=1 as the sampling period tends to zero are limiting intrinsic zeros (i.e., they do not appear if the continuous plant is zero-free). To prove that known result, it is not assumed as usual in the literature, that the plant is approximated by an integrator of order equal to its relative degree as the sampling period tends to zero. It Is also proved that limiting zeros at z=1 are present for any fractional zero-order hold (FROH), including the zero-order hold (ZOH) and the first-order hold (FOH), even when the continuous plant is of zero relative degree (i.e., biproper).