Asymptotic properties of zeros of multivariable sampled-data systems

When a continuous-time decouplable multivariable system with at least one of relative degrees greater than or equal to three is discretized using a zero-order hold, the resulting sampled-data model has an unstable zero for small sampling periods. Thus, attention is here focused on continuous-time systems with all relative degrees less than or equal to two from the viewpoint of stability of zeros of the corresponding sampled-data systems. This paper analyzes the zeros of the sampled-data models corresponding to the continuous-time multivariable 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.