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2009 | 19 | 2 | 255-261
Tytuł artykułu

Independence of asymptotic stability of positive 2D linear systems with delays of their delays

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.
Rocznik
Tom
19
Numer
2
Strony
255-261
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-10-06
poprawiono
2009-02-17
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok
Bibliografia
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  • Busłowicz, M. (2008a). Robust stability of convex combination of two fractional degree characteristic polynomials, Acta Mechanica et Automatica 2(2): 5-10.
  • Busłowicz, M. (2008b). Simple stability conditions for linear positive discrete-time systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(1): 325-328.
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  • Gałkowski, K. (2001). State Space Realizations of Linear 2D Systems with Extensions to the General nD (n>2) Case, Springer-Verlag, London.
  • Hmamed, A., Ait, Rami, M. and Alfidi, M. (2008). Controller synthesis for positive 2D systems described by the Roesser model, IEEE Transactions on Circuits and Systems, (submitted).
  • Kaczorek, T. (1985). Two-Dimensional Linear Systems, Springer-Verlag, Berlin.
  • Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2009a). Asymptotic stability of positive 2D linear systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(1), (in press).
  • Kaczorek, T. (2009b). Asymptotic stability of positive 2D linear systems, Proceedings of the 14-th Scientific Conference on Computer Applications in Electrical Engineering, Poznań, Poland, pp. 1-11.
  • Kaczorek, T. (2009c). LMI approach to stability of 2D positive systems, Multidimensional Systems and Signal Processing 20: 39-54.
  • Kaczorek, T. (2008a). Asymptotic stability of positive 1D and 2D linear systems, Recent Advances in Control and Automation, Academic Publishing House EXIT, pp. 41-52.
  • Kaczorek, T. (2008c). Checking of the asymptotic stability of positive 2D linear systems with delays, Proceedings of the Conference on Computer Systems Aided Science and Engineering Work in Transport, Mechanics and Electrical Engineering, TransComp, Zakopane, Poland, Monograph No. 122, pp. 235-250, Technical University of Radom, Radom.
  • Kaczorek, T. (2007). Choice of the forms of Lyapunov functions for positive 2D Roesser model, International Journal Applied Mathematics and Computer Science 17(4): 471-475.
  • Kaczorek, T. (2004). Realization problem for positive 2D systems with delays, Machine Intelligence and Robotic Control 6(2): 61-68.
  • Kaczorek, T. (1996). Reachability and controllability of nonnegative 2D Roesser type models, Bulletin of the Polish Academy of Sciences: Technical Sciences 44(4): 405-410.
  • Kaczorek, T. (2005). Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics 34(2): 411-423.
  • Kaczorek, T. (2006a). Minimal positive realizations for discretetime systems with state time-delays, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL 25(4): 812-826.
  • Kaczorek, T. (2006b). Positive 2D systems with delays, Proceedings of the 12-th IEEE/IFAC International Conference on Methods in Automation and Robotics, MMAR 2006, Międzyzdroje, Poland.
  • Kaczorek, T. (2003). Realizations problem for positive discretetime systems with delays, Systems Science 29(1): 15-29.
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  • Valcher, M.E. (1997). On the internal stability and asymptotic behavior of 2D positive systems, IEEE Transactions on Circuits and Systems-I 44(7): 602-613.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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