Inversion of sampled-data systemapproximates the continuous-time counterpart in a noncausal framework?

Although correspondence between the poles of a continuous-time and sampled-data system with a piecewise constant input is simple and desirable from the stability viewpoint, the relationship between zeros is intricate. Inversion of a sampled-data system is mostly unstable irrespective of the stability of the continuous-time counterpart. This makes it difficult to apply inversion-based control techniques such as perfect tracking, transient response shaping or iterative learning control to sampled-data systems. Although recently developed noncausal inversion techniques help us to circumvent unboundedness of the inversion caused by unstable zeros, whether the inversion of sampled-data systems approximates the continuous-time counterpart or not as the sample period is shortened is still to be determined. This article gives a positive conclusion to this problem. Key words: sampled-data systems; inverse system; transmission zeros; discrete-event dynamic system; feedforward control; nonminimum phase systems; zero-order hold; learning control