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2010 | 20 | 1 | 85-92
Tytuł artykułu

Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
Rocznik
Tom
20
Numer
1
Strony
85-92
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-03-19
poprawiono
2009-09-11
Twórcy
  • Faculty of Electical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland
  • Faculty of Electical Engineering, Białystok Technical University, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
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  • Bose, N. K. (1985). Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reidel Publishing Co., Dodrecht.
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  • Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263-269, DOI: 10.2478/v10006-009-0022-6.
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  • Fornasini, E. and Marchesini, G. (1978). Double indexed dynamical systems, Mathematical Systems Theory 12(1): 59-72.
  • Galkowski, K. (2001). State Space Realizations of Linear 2D Systems with Extensions to the General nD (n > 2) Case, Springer-Verlag, London.
  • Kaczorek, T. (1985). Two-Dimensional Linear Systems, Springer-Verlag, London.
  • 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. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2005). Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics 34(2): 411-423.
  • Kaczorek, T. (2007). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4): 139-143.
  • Kaczorek, T. (2008a). Asymptotic stability of positive 1D and 2D linear systems, in K. Malinowski and L. Rutkowski (Eds), Recent Advances in Control and Automation, Akademicka Oficyna Wydawnicza EXIT, Warsaw, pp. 41-52.
  • Kaczorek, T. (2008b). Asymptotic stability of positive 2D linear systems, Proceedings of the 13th Scientific Conference on Computer Applications in Electrical Engineering, Poznań, Poland, pp. 1-5.
  • Kaczorek, T. (2008c). Fractional 2D linear systems, Journal of Automation, Mobile Robotics & Intelligent Systems 2(2): 5-9.
  • Kaczorek, T. (2008d). Positive different orders fractional 2D linear systems, Acta Mechanica et Automatica 2(2): 51-58.
  • Kaczorek, T. (2009a). LMI approach to stability of 2D positive systems, Multidimensional Systems and Signal Processing 20(1): 39-54.
  • Kaczorek, T. (2009b). Positive 2D fractional linear systems, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL 28(2): 341-352.
  • Kaczorek, T. (2009c). Positivity and stabilization of 2D linear systems, Discussiones Mathematicae, Differential Inclusions, Control and Optimization 29(1): 43-52.
  • Kaczorek, T. (2009d). Stabilization of fractional discrete-time linear systems using state feedbacks, Proccedings of the LogiTrans Conference, Szczyrk, Poland, pp. 2-9.
  • Kurek, J. (1985). The general state-space model for a twodimensional linear digital systems, IEEE Transactions on Automatic Control AC-30(2): 600-602.
  • Miller, K. S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Willey, New York, NY.
  • Nashimoto, K. (1984). Fractional Calculus, Descartes Press, Koriyama.
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  • Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
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  • Twardy, M. (2007). An LMI approach to checking stability of 2D positive systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(4): 385-395.
  • 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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