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

Abstract

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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.

How to cite

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Antonis-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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  13. Vardulakis, A. (1991). Linear Multivariable Control: Algebraic Analysis and Synthesis Methods, Wiley, New York, NY. Zbl0751.93002
  14. Vardulakis, A. and Karcanias, N. (1983). Relations between strict equivalence invariants and structure at infinity of matrix pencils, IEEE Transactions on Automatic Control 28(4): 514-516. Zbl0519.93025
  15. Vardulakis, A., Limebeer, D. and Karcanias, N. (1982). Structure and Smith-MacMillan form of a rational matrix at infinity, International Journal of Control 35(4): 701-725. Zbl0495.93010
  16. Varga, A. (1989). Computation of irreducible generalized statespace realizations, Kybernetika 26(2): 89-106. Zbl0715.93030
  17. Verghese, G. (1978). Infinite Frequency Behavior in Dynamical Systems, Ph.D. thesis, Department of Electrical Engineering, Stanford University. 
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