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Nevanlinna-Pick interpolation developed from a topic in classical complexanalysis to a useful tool for solving various problems in control theory andelectrical engineering. Over the years many extensions of the original problemwere considered, including extensions to different function spaces,nonstationary problems, several variable settings and interpolation with matrixand operator points. Here we discuss a variation on Nevanlinna-Pickinterpolation for positive real odd functions evaluated in real matrix points.This problem was studied by Cohen and Lewkowicz using convex invertible conesand the Lyapunov order, but was never fully resolved. In this paper we presenta solution to this problem in a special case that we refer to as `suboptimal'based on connections with the classical case. The solution requires arepresentation of linear matrix maps going back to R.D. Hill and an analysis ofwhen positive linear matrix maps are completely positive, on which we reportedin earlier work and which we will briefly review here.

Convex invertible cones and Nevanlinna-Pick interpolation: The suboptimal case