We define Γ(E), a subset of C³, related to the structured singular value μ of 2x2 matrices. μ is used to analyse performance and robustness of linear feedback systems in control engineering. We find a characterisation for the elements of Γ(E) and establish a necessary and sufficient condition for the existence of an analytic function from the unit disc into Γ(E) satisfying an arbitrary finite number of interpolation conditions. We prove a Schwarz Lemma for Γ(E) when one of the points in Γ(E) is (0,0,0), then we show that in this case, the Carathéodory and Kobayashi distances between the two points in Γ(E) coincide. We also give a characterisation of the interior, the topological boundary and the distinguished boundary of Γ(E), then we define Γ(E)-inner functions and show that if there exists an analytic function from the unit disc into Γ(E) that satisfies the interpolating conditions, then there is a rational Γ(E)-inner function that interpolates.