A limiting property of the inverse of sampled-data systems on a finite-time interval

If one considers a sampled-data system derived from a continuous-time system with a relative degree of one or two on a finite-time interval, it is not simple to predict the behavior of the output of the inverse of the sampled-data system as the sampling period goes to zero. This is because the number of sample points increases while the zeros of the pulse-transfer function tend to the boundary between the stable and unstable areas. This paper shows that the output of the sampled-data inverse systems converges to the output of the continuous-time inverse systems independently of the stability of zeros.