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2008 | 18 | 2 | 223-228
Tytuł artykułu

Fractional positive continuous-time linear systems and their reachability

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new class of fractional linear continuous-time linear systems described by state equations is introduced. The solution to the state equations is derived using the Laplace transform. Necessary and sufficient conditions are established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems.
Słowa kluczowe
Rocznik
Tom
18
Numer
2
Strony
223-228
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-11-27
poprawiono
2008-02-02
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
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  • Kaczorek T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London
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  • Kaczorek T. (2007a). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4), (in press).
  • Kaczorek T.(2007b). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367.
  • Klamka J. (2002). Positive controllability of positive dynamical systems, Proceedings of American Control Conference, ACC-2002, Anchorage, AL, CD-ROM.
  • Klamka J. (2005). Approximate constrained controllability of mechanical systems, Journal of Theoretical and Applied Mechanics 43(3): 539-554.
  • Miller K.S. and B. Ross (1993). An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Willey, New York.
  • Moshrefi-Torbati M. and K. Hammond (1998). Physical and geometrical interpretation of fractional operators, Journal of the Franklin Institute 335B(6): 1077-1086.
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  • Ostalczyk P. (2004a). Fractional-order backward difference equivalent forms Part I Horner's form, IFAC Workshop on Fractional Differentation and its Applications, FDA'04, Bordeaux, France, pp. 342-347.
  • Ostalczyk P. (2004b), Fractional-order backward difference equivalent forms Part II Polynomial Form. Proceedings the 1st IFAC Workshop Fractional Differentation and its Applications, FDA'04, Bordeaux, France, pp. 348-353.
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  • Podlubny I. (2002). Geometric and physical interpretation of fractional integration and fractional differentation, Fractional Calculs and Applied Analysis 5(4): 367-386.
  • Podlubny I., L. Dorcak and I. Kostial (1997). On fractional derivatives, fractional order systems and $PI^λ D^μ$-controllers, Procedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4985-4990.
  • Reyes-Melo M.E., J.J. Martinez-Vega, C.A. Guerrero-Salazar and U. Ortiz-Mendez (2004). Modelling and relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order, Journal of Optoelectronics and Advanced Materials 6(3): 1037-1043.
  • Riu D., N. Retiére and M. Ivanes (2001). Turbine generator modeling by non-integer order systems, Proceedings of the IEEE International Conference on Electric Machines and Drives, IEMDC 2001, Cambridge, MA, USA, pp. 185-187.
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Typ dokumentu
Bibliografia
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