A characterisation of the gap metric for approximation problems

A characterization of the gap metric is developed in an operator theoretic setting, under assumptions regarding the existence of normalized strong right and left representations of the graph and a certain J-spectral factorization, known to hold for various classes of system. This new characterization 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