A fractional representation approach to the robust regulation problem for MIMO systems

TL;DR

This paper develops a unifying frequency domain framework for robust regulation of MIMO systems, introducing a new internal model principle, solvability conditions, and controller parametrization without coprime factorizations.

Contribution

It presents a novel fractional representation approach that generalizes robust regulation theory for MIMO systems, applicable to a broad class of systems with minimal assumptions.

Findings

New formulation of the internal model principle

Solvability conditions for robust regulation

Parametrization of all robust controllers

Abstract

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations, thus guaranteeing their applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.