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Determination of Singular Positive Realization of Improper Transfer Matrices of 2D Linear Systems

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Języki publikacji
EN
Abstrakty
EN
A new method for determination of singular positive realization of given improper transfer matrices of 2D linear systems is proposed. Necessary and sufficient conditions for the positivity of 2D singular models are established. It is shown that there exists a singular positive realization of a given improper transfer matrix. The procedure is illustrated by a numerical example.
Rocznik
Strony
83--104
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Warsaw University of Technology, Institute of Control and Industrial Electronics, Koszykowa 75, 00-662 Warsaw, POLAND, kaczorek@isep.pw.edu.pl
Bibliografia
  • [I] Bose N.K.: Applied Multidimensional Systems Theory, Van Nostrand Reinhold Co, New York 1982.
  • [2] Bose N.K.: Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reidel Publishing Co., 1985.
  • [3] Farina L. and Rinaldi S.: Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [4] Fornasini E. and Marchesini G.: State-space realization theory of two-dimensional filters, IEEE Trans. Autom. Contr., Vol. AC-21, 1976, pp. 484-491.
  • [5] Fornasini E. and Marchesini G.: Double indexed dynamical systems, Math. Sys. Theory, 12:59-72, 1978.
  • [6] Gałkowski K.: Elementary operation approach to state space realization of 2D systems, IEEE Trans. On Circuit and Systems, Vol. 44, 1997, pp. 120-129.
  • [7] Gałkowski K.: State space realizations of linear 2D systems with extensions to the general nD (n > 2) case, Springer Verlag London 2001.
  • [8] Kaczorek T.: Two-Dimensional Linear Systems, Springer Verlag, Berlin 1985. [9] Kaczorek T.: Positive ID and 2D systems, Springer Verlag, London 2002.
  • [10] Kaczorek T.: Reachability and controllability of non-negative 2D Roesser type models, Buli. Acad. Poi. Sci. Ser. Sci. Techn., Vol. 44, No 4, 1996, pp. 405-410.
  • [11] Kaczorek T.: Some recent developments in positive systems, Proc. 7th Conference of Dynamical Systems Theory and Applications, pp. 25-35, Łódź 2003.
  • [12] Kaczorek T.: Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics, Vol. 34, No 2, 2005, pp. 411-423.
  • [13] Kaczorek T.: Minimal positive realizations for discrete-time systems with state time-delays, The Inter. J. for Comp. and Math. in Elec. and Electronics Eng., COMPEL Vol. 25, No. 4, pp. 812-826, 2006.
  • [14] Kaczorek T.: Realization problem for positive discrete-time systems with delays, System Science, Vol. 29, No. 1, 2003, pp. 15-29.
  • [15] Kaczorek T.: Realization problem for a class of positive continuous-time systems with delays, Int. J. Appl. Math. Comp. Sci., Vol. 15, No. 4, 2005, pp. 101-107.
  • [16] Kaczorek T.: Realization problem for a class of positive continuous-time systems with delays, Int. J. Appl. Math Comput. Sci, 2005, Vol. 15, No 4, pp. 101-107
  • [17] Kaczorek T.: Positive 2D systems with delays. Proc. of 12th MMAR Conf, Międzyzdroje 2006, Poland.
  • [18] Kaczorek T.: State vańable diagram method for determination ofpositive singular realizations of 2D systems with delays. Submitted to Multidimensional Systems and Signal Processing 2006.
  • [19] Kaczorek T.: Realization problem for positive 2D hybrid systems. Submitted to COMPEL 2006.
  • [20] Kaczorek T. and Busłowicz M.: Minimal realization for positive multivariable linear systems with delay, Int. J. Appl. Math. Comput. Sci., 2004, Vol. 14, No 2, pp. 181-187.
  • [21] Klamka J.: Controllability of dynamical systems, Kluwr Academic Publ., Dordrecht, 1991.
  • [22] Kurek J.: The generał state-space model for a two-dimensional linear digital systems, IEEE Trans. Autom. Contr. AC-30, June 1985, pp. 600-602
  • [23] Roesser R.P.: A discrete state-space model for linear image processing, IEEE Trans, on Automatic Control, AC-20, 1, 1-10, 1975
  • [24] Valcher M.E.: On the initial stability and asymptotic behavior of 2D positive systems, IEEE Trans. On Circuits and Systems -1, Vol. 44, No 7,1997, pp. 602-613
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD5-0011-0007
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