# Robust Regulation of MIMO systems: A Reformulation of the Internal Model Principle

## TL;DR

This paper reformulates the internal model principle for MIMO systems using a general factorization approach, broadening its theoretical foundation and applicability beyond classical coprime factorizations.

## Contribution

It introduces a new formulation of the internal model principle based on fractional ideals, removing restrictions of classical methods.

## Key findings

- New formulation broadens applicability of the internal model principle.
- Relates the reformulation to classical results, ensuring consistency.
- Provides a more general theoretical framework for robust regulation.

## Abstract

The internal model principle is a fundamental result stating a necessary and sufficient condition for a stabilizing controller to be robustly regulating. Its classical formulation is given in terms of coprime factorizations and the largest invariant factor of the signal generator which sets unnecessary restrictions for the theory and its applicability. In this article, the internal model principle is formulated using a general factorization approach and the generators of the fractional ideals generated by the elements of the signal generator. The proposed results are related to the classical ones.