A Nested Feedback Loop Decomposition for the Reduction of Linear Multi-variable Systems

Previous results on the reduction of single-input/single-output systems are extended to the case of square invertible multi-variable systems. It is shown that such systems have a unique decomposition in the form of a forward and a feedback path each having special properties relating to the invariant zero's of the original system. Under certain generic conditions this decomposition this decomposition can be extended to yield a representation of the system as a nested sequence of feedback loops. This provides a convenient method of deriving reducing-order models, which will give good matching of the asymptotic system root-locus and open-and-closed-loop system dynamics and hence will be a valid tool in closed-loop controller design.