Minimal order, measurable output, disturbance rejection feedback compensators

A new necessary and sufficient condition is established for existence of a measureable output disturbance rejection feed-back for a given multivariable linear system with disturbances. If the developed condition does not hold a method of determination of extension of the given system via a dynamic compensator is presented. An upper and lower bound on a minimal extension is established. Stability of the closed loop system is considered and structure of the closed loop characteristic polynomial is discussed. The developed results are applied to solve rational matrix equations G(s)X(s)N(s)+H(s) = 0. It is shown that existence of a proper transfer matrix solution X(s) to G(s)X(s)N(s) + H(s) = 0 is equivalent with existence of a measurable output disturbance rejection feedback for a certain multivariable linear system with disturbances.