Algebraic Theory of Linear Multivariable Feedback Systems

This paper presents an algebraic theory for analysis and design of linear multivariable feedback systems, which is sufficiently general to apply to lumped and distributed systems as well as continuous or discrete time. By use of a controller with two vector inputs, results are obtained which give global parametrizations of all I/O and D/O maps achievable for a given plant by a stabilizing compensator. Also given are conditions sufficient for the asymptotic tracking of a class of inputs. Sufficient conditions for the robustness of the above results are also presented. In the special case of lumped systems it is shown that the design theory can be simplified to involve manipulations of polynomial matrices only.