# "Wrong" Side Interpolation by Low Degree Positive Real rational Functions

## TL;DR

This paper demonstrates that positive real rational functions of degree at most m can interpolate m nodes in the left half-plane to any target points in the complex plane, providing a new parametrization method.

## Contribution

It introduces a novel interpolation method using positive real rational functions and a simple parametrization for a large subset of such functions.

## Key findings

- Any set of m nodes in the left half-plane can be mapped to any complex points by degree-m positive real functions.
- A new parametrization in R^{2m+3} for a large subset of these interpolating functions.
- The approach combines polynomial interpolation with structural properties of positive real functions.

## Abstract

Using polynomial interpolation, along with structural properties of the family of positive real rational functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the complex plane by rational positive real functions whose degree is at most m. Moreover, we introduce an easy-to-find parametrization in $R^{2m+3}$ of a large subset of these interpolating functions.