A characterisation of the gap metric for approximation problems

Abstract

A characterisation of the gap metric is developed in an operator theoretic setting, under assumptions regarding the existence of normalised strong right and left representations of the graph and a certain J-spectral factorisation, known to hold for various classes of system. This new characterisation appears to be useful within the context of model approximation problems because it is equivalent to bounding the gain of a linear fractional interconnection, which is well-studied in the literature of modern control theory. © 2006 IEEE.