Asymptotic properties of zeros of sampled-data systems

When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold, at least one of the zeros of the resulting sampled-data model is unstable for small sampling periods. Thus, attention is here focused on continuous-time systems with relative degree less than or equal to two. This paper analyzes the zeros of the sampled-data models corresponding to the continuous-time systems mentioned above and gives approximate expressions of the zeros as power series expansions with respect to a sampling period. Further, the stability of the zeros is discussed for small sampling periods and a new stability condition is derived.