# Multivariable analytic interpolation with complexity constraints: A modified Riccati approach

## TL;DR

This paper introduces a new multivariable analytic interpolation method with complexity constraints, extending previous scalar results, and employs a homotopy continuation algorithm to solve Riccati-type matrix equations.

## Contribution

It generalizes scalar interpolation techniques to multivariable cases, addressing new challenges and providing an algorithm for solving associated Riccati equations.

## Key findings

- Developed a new multivariable interpolation method.
- Extended scalar results to multivariable systems.
- Provided an algorithm based on homotopy continuation for Riccati equations.

## Abstract

Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the scalar case. This turns out to be quite nontrivial, as it poses many new problems. A basic step in the procedure is to solve a Riccati type matrix equation. To this end, an algorithm based on homotopy continuation is provided.