[k,ksup,omega] = kappa(P1,P2) or [k,ksup] = kappa(P1,P2,omega) returns the frequency-wise v-Gap between the dynamical systems P1 and P2 as defined in Vinnicombe (2000, p.123). This essentially gives a frequency-wise measure of the difference between two plants and the worst-case drop in closed-loop performance if a controller designed for one system is used with the other. Following the reference, ksup is the supremum of k if [P2, -P1'] has the same number of open RHP poles as [P1, -P1'], otherwise it will be set to unity.
kappa(P1,P2) or kappa(P1,p2,omega) without any output arguments will display the results in graphical form.
1. Vinnicombe, G. (2000) Uncertainty and Feedback: H-Infinity Loop-Shaping and the v-Gap Metric. London: Imperial College
See also: sigma, rho.