Limiting zeros of a class of sampled multivariable systems

It is desirable that a plant has all stable zeros in many control schemes. Stability conditions of sampled multivariable systems have been considered by (Hayakawa et al., 1983). They have shown how the zeros of the sampled system are located when the sampling period tends to zero. Their result has shown that those zeros corresponding to continuous-time zeros approach 1 and the remaining zeros converge to the specific constant values determined by some definite polynomials. The stability condition of the former zeros has been given by them. Some zeros of the latter reach -1 and there remains the possibility that they approach from inside the unit circle. It is an unresolved problem. The purpose of this paper is to give an answer to this problem. It shows when the zero of sampled two-input two-output, third order systems goes to -1 from inside the unit circle