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General Response Formula for Fractional 2D Continuous-Time Linear Systems Described by the Roesser Model

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Języki publikacji
EN
Abstrakty
EN
A new class of fractional two-dimensional (2D) continuous-time linear systems is introduced. The general response formula for the system is derived using a 2D Laplace transform. It is shown that the classical Cayley-Hamilton theo- rem is valid for such class of systems. Usefulness of the general response formula to obtain a solution of the system is discussed and illustrated by a numerical example.
Rocznik
Strony
112--116
Opis fizyczny
Bibliogr. 21 poz., Rys., Wykr.
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autor
Bibliografia
  • 1. Bose N. K. (1982), Applied Multidimensional Systems Theory, Van Nonstrand Reinhold Co., New York.
  • 2. Bose N. K. (1985), Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reidel Publish. Co., Dodrecht.
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  • 4. Fornasini E., Marchesini G. (1976), State-space realization theory of two-dimensional filters, IEEE Trans. Automat. Contr., Vol. AC-21, No. 4, 484-491.
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  • 6. Gałkowski K. (2001), State-space Realizations of Linear 2-D Systems with Extensions to the General nD ( n > 2 ) Case, Springer-Verlag, London.
  • 7. Kaczorek T. (1985), Two-Dimensional Linear Systems, Springer-Verlag, London.
  • 8. Kaczorek T. (2001), Positive 1D and 2D Systems, SpringerVerlag, London.
  • 9. Kaczorek T. (2008a), Fractional 2D linear systems, Automation , Mobile Robotics and Intelligent systems, Vol. 2, No. 2, 5-9.
  • 10. Kaczorek. T. (2008b), Positive different orders fractional 2D linear systems, Acta Mechanica et Automatica, Vol. 2, No. 2, 51-58.
  • 11. Kaczorek T. (2009), Positive 2D fractional linear systems, COMPEL, Vol. 28, No. 2, 341-352.
  • 12. Kaczorek T. (2011), Selected Problems in Fractional Systems Theory, Springer-Verlag.
  • 13. Kaczorek T., Rogowski K. (2010), Positivity and stabilization of fractional 2D linear systems described by the Roesser model, Int. J. Appl. Math. Comput. Sci., Vol. 20, No. 1, 85-92.
  • 14. Kurek J. (1985), The general state-space model for twodimensional linear digital systems, IEEE Trans. Automat. Contr., Vol. AC-30, No. 2, 600-602.
  • 15. Miller K. S., Ross B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, J. Willey, New York.
  • 16. Nashimoto K. (1984), Fractional Calculus, Descartes Press, Kariyama.
  • 17. Oldham K. B., Spanier J. (1974), The Fractional Calculus, Academic Press, New York.
  • 18. Ostalczyk P. (2008), Epitome of the Fractional Calculus: Theory and its Applications in Automatics, Wydawnictwo Politechniki Łódzkiej, Łódź (in polish).
  • 19. Podlubny I. (1999), Fractional Differential Equations, Academic Press, San Diego.
  • 20. Roesser R. (1975), A discrete state-space model for linear image processing, IEEE Trans. Automat. Contr., vol. AC-20, No. 1, 1-10.
  • 21. Rogowski K. (2011), Positivity and stability of fractional 2D Lyapunov systems described by the Roesser model, Bull. Pol. Acad. Sci. Techn., (in press).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0051-0028
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