# Partial Realization Theory and System Identification Redux

## TL;DR

This paper revisits a nonstandard matrix Riccati equation from 20 years ago, deriving it anew within system identification, and demonstrating its universality for solving various analytic interpolation problems in control systems.

## Contribution

It provides a new derivation of a nonstandard Riccati equation and shows its broad applicability to general analytic interpolation problems in control theory.

## Key findings

- The Riccati equation is universal for interpolation problems.
- The derivation connects realization theory with system identification.
- It addresses a question posed by R.E. Kalman in the 1970s.

## Abstract

Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.