Robust approximate modelling of stable linear systems†

Publisher Website
Google Scholar
Abstract
Robust approximation and worst-case approximate modelling of stable shift-invariant systems from corrupted transfer function estimates are studied in the H ∞ sense. Connections between the problem formulations of the present work and certain problems of worst-case system identification, notably the Helmicki-Jacobson-Nett problem formulation for identification in H ∞, are established. Issues of model set selection are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in then-width sense. A notion of robust convergence is defined so that any untuned approximation method satisfying it has a generic well-posedness property for systems in the disk algebra. The existence of robustly convergent approximation methods based on any complete model set in the disk algebra is shown in a constructive way. A framework is given in which approximate models can be obtained as stable perturbations of the true system: these can be combined with the classical Fejér and de la Vallée-Pous-sin polynomial approximation operators to provide robustly convergent approximation methods. Furthermore, concrete results are given for the fundamental problem of model reduction from corrupted transfer function estimates or from experimentally obtained models for the optimal Hankel norm approximation method and for a least squares method.

This publication has 17 references indexed in Scilit: