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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  1. Bosgra, O. and Van Der Weiden, A. (1981). Realizations in generalized state-space form for polynomial system matrices and the definitions of poles, zeros and decoupling zeros at infinity, International Journal of Control 33(3): 393-411. Zbl0464.93021
  2. Christodoulou, M. and Mertzios, B. (1986). Canonical forms for singular systems, Proceedings of the of 25th IEEE Conference on Decision and Control (CDC), Athens, Greece, pp. 2142-2143. 
  3. Cobb, D. (1984). Controllability, observability, and duality in singular systems, IEEE Transactions on Automatic Control 29(12): 1076-1082. 
  4. Conte, G. and Perdon, A. (1982). Generalized state space realizations of non-proper rational transfer functions, Systems and Control Letters 1(4): 270-276. Zbl0473.93023
  5. Gantmacher, F. (1959). The Theory of Matrices, Chelsea Publishing Company, New York, NY. Zbl0085.01001
  6. Karampetakis, N. (1993). Notions of Equivalence for Linear Time Invariant Multivariable Systems, Ph.D. thesis, Department of Mathematics, Aristotle University of Thessaloniki. 
  7. Lewis, F. (1986). A survey of linear singular systems, Circuits, Systems, and Signal Processing 5(1): 3-36. Zbl0613.93029
  8. Lewis, F., Beauchamp, G. and Syrmos, V. (1989). Some useful aspects of the infinite structure in singular systems, Proceedings of the International Symposium MTNS-89, Amsterdam, The Netherlands, pp. 263-270. Zbl0726.93035
  9. Misra, P. and Patel, R. (1989). Computation of minimal-order realizations of generalized state-space systems, Circuits, Systems, and Signal Processing 8(1): 49-70. Zbl0681.93013
  10. Rosenbrock, H. (1970). State Space and Multivariable Theory, Nelson, London. Zbl0246.93010
  11. Rosenbrock, H. (1974). Structural properties of linear dynamical systems, International Journal of Control 20(2): 191-202. Zbl0285.93019
  12. Vafiadis, D. and Karcanias, N. (1995). Generalized state-space realizations from matrix fraction descriptions, IEEE Transactions on Automatic Control 40(6): 1134-1137. Zbl0829.93011
  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. 
  18. Verghese, G., Levy, B. and Kailath, T. (1981). A generalized state-space for singular systems, IEEE Transactions on Automatic Control 26(4): 811-831. Zbl0541.34040

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