Synthesis of linear multivariable regulators

This paper generalizes the results obtained by the authors in [1] and presents new results on the construction of proper controllers for linear multivariable regulators. These results may lead to efficient computation methods that do not involve Smith forms or the order relations used in [1] to construct proper controllers. The methods are based on the recently developed theory of Λ-generalized polynomials [2]. We discuss several numerical algorithms and how they can be applied to the regulator problem. We also point out an important computational problem in need of an efficient numerical algorithm.