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Asymptotic stability of positive 2D linear systems with delays

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EN
Abstrakty
EN
New necessary and sufficient conditions for the asymptotic stability of positive 2D linear systems with delays described by the general model, Fornasini-Marchesini models and Roesser model are established. It is shown that checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to the checking of the asymptotic stability of corresponding positive ID linear systems without delays. The efficiency of the new criterions is demonstrated on numerical examples.
Twórcy
autor
  • Institute of Control and Industrial Electronics, Warsaw University of Technology, 75 Koszykowa St., 00-662 Warsaw, Poland, kaczorek@isep.pw.edu.pl
Bibliografia
  • [1] RP. Roesser, "A discrete state-space model for linear image processing", IEEE Trans. Autom. Contr. AC-20, 1-10 (1975).
  • [2] E. Fornasini and G. Marchesini, "State-space realization theory of two-dimensional filters", IEEE Trans, Autom. Contr. AC-21, 481-491 (1976).
  • [3] E. Fornasini and G. Marchesini, "Double indexed dynamical systems", Math. Sys. Theory 12, 59-72 (1978).
  • [4] J. Kurek, "The general state-space model for a two-dimensional linear digital systems", IEEE Trans. Autom. Contr. AC-30, 600-602 (1985).
  • [5] T. Kaczorek, "Reachability and controllability of non-negative 2D Roesser type models", Bull. Pol. Ac.: Tech. 44 (4), 405-410 (1996).
  • [6] M.E. Va1cher, "On the internal stability and asymptotic behavior of 2D positive systems", IEEE Trans. on Circuits and Systems 44 (7), 602-613 (1997).
  • [7] T. Kaczorek, "Reachability and minimum energy control of positive 2D systems with delays", Control and Cybernetics 34 (2),411-423 (2005).
  • [8] T. Kaczorek, Positive ID and 2D Systems, Springer-Verlag, London, 200l.
  • [9] N.K. Bose, Applied Multidimensional System Theory, Van Nostrand Reinho1d Co, New York, 1982.
  • [10] N.K. Bose, Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reide1 Publishing Co., New York, 1985.
  • [11] K. Galkowski, Elementary operation approach to state space realization of 2D systems, IEEE Trans. on Circuit and Systems 44, 120-129 (1997).
  • [12] K. Galkowski, State Space Realizations of Linear 2D Systems with Extensions to the General nD (n > 2) Case, Springer Verlag, London, 200l.
  • [13] T. Kaczorek, Two-dimensional Linear Systems, Springer Ver1ag, Berlin, 1985.
  • [14] L. Farina and S. Rina1di, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [15] T. Kaczorek, "Choice of the forms of Lyapunov functions for positive 2D Roesser model", Int. J. Applied Math. and Comp. Science 17 (4), 471-475 (2007).
  • [16] T. Kaczorek, "Positive 2D systems with delays", MMAR 12th IEEE IFAC Int. Conf. Methods in Automation and Robotics, 28-31 (2006).
  • [17] T. Kaczorek, "Minimal positive realizations for discrete-time systems with state time-delays", The Int. J. Comp. and Math. in Elec. and Electronics Eng. 25 (4), 812-826 (2006).
  • [18] T. Kaczorek, "Realizations problem for positive discrete-time systems with delays", Systems Science 29 (1), 15-29 (2003).
  • [19] T. Kaczorek, "Realization problem for positive 2D systems with delays", Machine Intelligence and Robotic Control 6 (2), 61-68 (2004).
  • [20] A. Hmamed, M. Ait Rami, and M. A1fidi, "Controller synthesis for positive 2D systems described by the Roesser model", IEEE Trans. on Circuits and Systems, (2009), to be published.
  • [21] T. Kaczorek, "Asymptotic stability of positive 2D linear systems, Proc. XIII Conf. Computer Applications in Electrical Engineering, CD-ROM (2008).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG5-0038-0031
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