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2009 | 19 | 1 | 77-88
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
19
Numer
1
Strony
77-88
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-02-15
Twórcy
  • Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54 006, Greece
  • Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54 006, Greece
  • Department of Sciences, Technical Educational Institute of Thessaloniki, Sindos 574 00, Greece
  • General Department of Applied Science, Technical University of Chalkis, Psahna 34 400, Eubea, Greece
Bibliografia
  • 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.
  • 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.
  • Cobb, D. (1984). Controllability, observability, and duality in singular systems, IEEE Transactions on Automatic Control 29(12): 1076-1082.
  • Conte, G. and Perdon, A. (1982). Generalized state space realizations of non-proper rational transfer functions, Systems and Control Letters 1(4): 270-276.
  • Gantmacher, F. (1959). The Theory of Matrices, Chelsea Publishing Company, New York, NY.
  • Karampetakis, N. (1993). Notions of Equivalence for Linear Time Invariant Multivariable Systems, Ph.D. thesis, Department of Mathematics, Aristotle University of Thessaloniki.
  • Lewis, F. (1986). A survey of linear singular systems, Circuits, Systems, and Signal Processing 5(1): 3-36.
  • 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.
  • 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.
  • Rosenbrock, H. (1970). State Space and Multivariable Theory, Nelson, London.
  • Rosenbrock, H. (1974). Structural properties of linear dynamical systems, International Journal of Control 20(2): 191-202.
  • Vafiadis, D. and Karcanias, N. (1995). Generalized state-space realizations from matrix fraction descriptions, IEEE Transactions on Automatic Control 40(6): 1134-1137.
  • Vardulakis, A. (1991). Linear Multivariable Control: Algebraic Analysis and Synthesis Methods, Wiley, New York, NY.
  • 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.
  • 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.
  • Varga, A. (1989). Computation of irreducible generalized statespace realizations, Kybernetika 26(2): 89-106.
  • Verghese, G. (1978). Infinite Frequency Behavior in Dynamical Systems, Ph.D. thesis, Department of Electrical Engineering, Stanford University.
  • Verghese, G., Levy, B. and Kailath, T. (1981). A generalized state-space for singular systems, IEEE Transactions on Automatic Control 26(4): 811-831.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv19i1p77bwm
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