On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

Abstract

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space SystemsWe review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of anirreducible-at-infinitygeneralized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts ofirreducibilityandminimalityof generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts ofdynamicandnon-dynamicvariables appearing in generalized state space realizations are also examined.