Coprime factorisation and gap metric for nonlinear systems

Several graph and gap metrics are defined using normalized coprime factorisations for nonlinear signal operators. Their relation to the gap metrics of a Georgiou and Smith type are discussed. It is proved that the topological structures of the two classes of metrics are equivalent. Formulas for a ρ-gap metric and a nonlinear generalization of the Georgiou-type gap metric are shown to be equal.