Boundary Nevanlinna--Pick Interpolation with Prescribed Peak Points. Application to Impedance Matching

Abstract

We study a generalized Nevanlinna--Pick interpolation problem on the half-plane for rational functions of prescribed degree, where peak points are imposed and interpolation conditions may lie on the real axis. This generalizes previous work by Georgiou, Byrnes, Lindquist, and Megretski. The problem is motivated by the issue of broadband matching in electronics and microwave system design. We prove existence and uniqueness of a solution by differential-topological techniques. The approach is put to work numerically on a real example, using a continuation method.