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 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.
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SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2017, 〈10.1137/16M1085577〉
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Laurent Baratchart, Martine Olivi, Fabien Seyfert. Boundary nevanlinna-pick interpolation with prescribed peak points. Application to impedance matching. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2017, 〈10.1137/16M1085577〉. 〈hal-01377782v2〉

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