# A fractional representation approach to the robust regulation problem for SISO systems

## TL;DR

This paper introduces an algebraic fractional representation method for solving the robust regulation problem in SISO systems, especially those lacking coprime factorizations, providing a unified framework and controller parametrization.

## Contribution

It develops a novel algebraic approach using fractional representations to address robust regulation without requiring coprime factorizations, extending the internal model principle.

## Key findings

- Necessary and sufficient conditions for robust regulation are established.
- All robust controllers can be explicitly parameterized.
- The approach applies to a broad class of systems without coprime factorizations.

## Abstract

The purpose of this article is to develop a new approach to the robust regulation problem for plants which do not necessarily admit coprime factorizations. The approach is purely algebraic and allows us dealing with a very general class of systems in a unique simple framework. We formulate the famous internal model principle in a form suitable for plants defined by fractional representations which are not necessarily coprime factorizations. By using the internal model principle, we are able to give necessary and sufficient solvability conditions for the robust regulation problem and to parameterize all robustly regulating controllers.