Geodesic
On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems
International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 77-88.

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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 pointed out and the associated concepts of dynamic and non-dynamic variables appearing in generalized state space realizations are also examined.
Keywords: polynomial matrices, realization theory, minimality, irreducibility, generalized state space, infinite decoupling zeros
Mots-clés : macierz wielomianowa, nierozkładalność, przestrzeń stanu 
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Vardulakis, A. I. G.; Karampetakis, N. P.; Antoniou, E. N.; Tictopoulou, E. On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/IJAMCS_2009_19_1_a6/

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