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

If a sampled-data linear system is considered on a fixed finite time interval, it is not a trivial matter to determine whether the output of the inverse of the system converges or diverges as the sampling period goes to 0 because the number of sample points increases while some zeros of the pulse transfer function tend to the boundary between the stable and unstable areas. This paper discusses the inverse of sampled-data systems obtained from linear continuous-time systems of relative degree 2. It is demonstrated that the inverse of sampled-data systems converges to the inverse continuous-time systems on a given finite time interval, even if the system zeros are unstable.