Analytic study on the intrinsic zeros of sampled-data systems

This paper investigates the properties of the mapping from the simple zero gamma of a scalar continuous-time system to the corresponding zero Gamma(T) of the sampled-data system that results by its discretization using a zero-order hold, where T is the sampling period. It is shown that Gamma(T) admits a Taylor expansion with respect to T; and that it coincides with that of exp(gamma T) at least up to the second-order term, in general, and at least up to the third-order term if the relative degree of the continuous-time system is greater than or equal to two. The result is applied to derive a new stability condition of Gamma(T) for sufficiently small sampling periods.