Boundary nevanlinna-pick interpolation with prescribed peak points. Application to impedance matching

Laurent Baratchart (1) , Martine Olivi (1) , Fabien Seyfert (1)

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing

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 T. Giorgiou, C. Byrnes, A Lindquist and A. 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.

Domaines: Mathématiques [math]; Analyse fonctionnelle [math.FA]

Laurent Baratchart, Martine Olivi, Fabien Seyfert. Boundary nevanlinna-pick interpolation with prescribed peak points. Application to impedance matching. 2016. ⟨hal-01377782v1⟩