### On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems

Antonis-Ioannis G. Vardulakis, Nicholas P. Karampetakis, Efstathios N. Antoniou, Evangelia Tictopoulou (2009)

International Journal of Applied Mathematics and Computer Science

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We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized 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 of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is...