Robust approximation and identification in H∞

Robust approximation and identification of stable shiftinvariant systems is studied in the H
^∞
sense using a stable perturbation set-up. Issues of model set selection tion are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in the n-width sense. A general construction of interest to identification theory using ϵ-nets provides near-optimal identification methods tuned to the a priori knowledge about the system. A notion of robust convergence is defined so that any untuned identification method satisfying it has a generic well-posedness property for systems in the disk algebra. The existence of robustly convergent identification methods based on any complete model set in the disk algebra is established. It is also shown that the classical Fejér and de la Vallée-Poussin polynomial approximation operators provide robustly convergent identification methods. Furthermore, a result is given for optimal Hankel norm model reduction from experimentally obtained models.