This paper studies properties of limiting zeros, which are defined as zeros of sampled-data systems resulting from continuous-time scalar systems preceded by zero-order hold with sufficiently small sampling period. Firstly, the regions are clarified in which the limiting zeros corresponding to the zeros of the original continuous-time system should exist. Secondly, other limiting zeros are studied, which are always yielded when the relative degree of the original continuous-time system is greater than or equal to 2 and do not have any counterpart of the original continuous-time system. To be specific, stability of such a zero is studied for the case where the relative degree of the original continuous-time system is 2. Using the above two results, a condition is derived on which all the limiting zeros are stable.
Furthermore, relating to strong stabilizability of sampled-data systems, which is defined as possibility of being stabilized by a stable controller and is equivalent to the parity interlacing property (a condition on the location of real zeros and real poles), some criteria are given with which to examine whether limiting zeros are real or not.