A fractional representation approach to the robust regulation problem for multi-input multi-output systems

The aim of this article is in developing unifying frequency domain theory for robust regulation of multi-input multi-output systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parameterization 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.