# 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

International Journal of Applied Mathematics and Computer Science (2009)

- Volume: 19, Issue: 1, page 77-88
- ISSN: 1641-876X

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topAntonis-Ioannis G. Vardulakis, et al. "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 19.1 (2009): 77-88. <http://eudml.org/doc/207924>.

@article{Antonis2009,

abstract = {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.},

author = {Antonis-Ioannis G. Vardulakis, Nicholas P. Karampetakis, Efstathios N. Antoniou, Evangelia Tictopoulou},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {polynomial matrices; realization theory; minimality; irreducibility; generalized state space; infinite decoupling zeros},

language = {eng},

number = {1},

pages = {77-88},

title = {On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems},

url = {http://eudml.org/doc/207924},

volume = {19},

year = {2009},

}

TY - JOUR

AU - Antonis-Ioannis G. Vardulakis

AU - Nicholas P. Karampetakis

AU - Efstathios N. Antoniou

AU - Evangelia Tictopoulou

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2009

VL - 19

IS - 1

SP - 77

EP - 88

AB - 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.

LA - eng

KW - polynomial matrices; realization theory; minimality; irreducibility; generalized state space; infinite decoupling zeros

UR - http://eudml.org/doc/207924

ER -

## References

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