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2010 | 20 | 3 | 507-512
Tytuł artykułu

Similarity transformation of matrices to one common canonical form and its applications to 2D linear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of a common canonical form for a sequence of square matrices is introduced. Necessary and sufficient conditions for the existence of a similarity transformation reducing the sequence of matrices to the common canonical form are established. It is shown that (i) using a suitable state vector linear transformation it is possible to decompose a linear 2D system into two linear 2D subsystems such that the dynamics of the second subsystem are independent of those of the first one, (ii) the reduced 2D system is positive if and only if the linear transformation matrix is monomial. Necessary and sufficient conditions are established for the existence of a gain matrix such that the matrices of the closed-loop system can be reduced to the common canonical form.
Rocznik
Tom
20
Numer
3
Strony
507-512
Opis fizyczny
Daty
wydano
2010
otrzymano
2010-02-15
poprawiono
2010-05-17
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • Ansaklis, P.J. and Michel, N. (1997). Linear Systems, McGrowHill, New York, NY.
  • Basile, G. and Marro, G. (1969). Controlled and conditioned invariant subspaces in linear system theory, Journal of Optimization Theory and Applications 3(5): 306-315.
  • Basile, G. and Marro, G. (1982). Self-bounded controlled invariant subspaces: A straightforward approach to constrained controllability, Journal of Optimization Theory and Applications 38(1): 71-81.
  • Conte, G. and Perdon, A. (1988). A geometric approach to the theory of 2-D systems, IEEE Transactions on Automatics Control AC-33(10): 946-950.
  • Conte, G., Perdon, A. and Kaczorek, T. (1991). Geometric methods in the theory of singular 2D linear systems, Kybernetika 27(3): 262-270.
  • Fornasini, E. and Marchesini, G. (1978). Doubly-indexed dynamical systems: State-space models and structural properties, Mathematical System Theory 12: 59-72.
  • Kaczorek, T. (1992). Linear Control Systems, Vol. 2, Wiley, New York, NY.
  • Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2007). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London.
  • Kailath, T. (1980). Linear Systems, Prentice Hall, Englewood Cliffs, NJ.
  • Karmanciolu, A. and Lewis, F.L. (1990). A geometric approach to 2-D implicit systems, Proceedings of the 29th Conference on Decision and Control, Honolulu, HI, USA.
  • Karmanciolu, A. and Lewis, F.L. (1992). Geometric theory for the singular Roesser model, IEEE Transactions on Automatics Control AC-37(6): 801-806.
  • Kurek, J. (1985). The general state-space model for a twodimensional linear digital systems, IEEE Transactions on Automatics Control AC-30(6): 600-602.
  • Malabre, M., Martínez-García, J. and Del-Muro-Cuéllar, B. (1997). On the fixed poles for disturbance rejection, Automatica 33(6): 1209-1211.
  • Ntogramatzis, L. (2010). A geometric theory for 2-D systems, Multidimensional Systems and Signal Processing, (submitted).
  • Roesser, R.P. (1975). A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control AC-20(1): 1-10.
  • Wonham, W.M. (1979). Linear Multivariable Control: A Geometric Approach, Springer, New York, NY.
  • Żak S. (2003). Systems and Control, Oxford University Press, New York, NY.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv20i3p507bwm
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