Stable inversion for nonminimum phase sampled-data systems and its relation with the continuous-time counterpart

Stable inversion technique has been developed as an approach to exact output tracking, which is feasible even if the transfer function of the plant is nonminimum phase. Its key idea is separating the plant into minimum and nonminimum phase parts and applying causal and noncausal inverse mappings to the former and the latter, respectively. Although similar idea is straightforwardly extended to discrete-time systems, it is not very clear whether sampled-data stable inversion approximates the continuous-time counterpart. This is because there is no simple relation between zeros of the continuous-time transfer function and zeros of the corresponding pulse transfer function. The sampled-data stable inversion can be noncausal even if continuous-time stable inversion is causal. This paper demonstrate that the sampled-data stable inversion simply converges to the continuous-time counterpart as the sampling period goes to 0. This result guarantees that one can achieve exact output tracking with arbitrary high precision by eliminating output error only at sample points with a sufficiently small sampling period. Moreover, the result also supports feasibility of adjoint-type iterative learning control which can asymptotically obtain stable inversion through trial iterations.