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2009 | 19 | 1 | 89-93
Tytuł artykułu

Reachability of cone fractional continuous-time linear systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new class of cone fractional continuous-time linear systems is introduced. Necessary and sufficient conditions for a fractional linear system to be a cone fractional one are established. Sufficient conditions for the reachability of cone fractional systems are given. The discussion is illustrated with an example of linear cone fractional systems.
Słowa kluczowe
Rocznik
Tom
19
Numer
1
Strony
89-93
Opis fizyczny
Daty
wydano
2009
otrzymano
2008-04-21
poprawiono
2008-06-08
Twórcy
  • Faculty of Electrical Engineering, Białystok Technical University, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
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  • Gałkowski, K. (2005). Fractional polynomials and nD systems. Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS'2005, Kobe, Japan, CD-ROM.
  • Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
  • Kaczorek, T. (2006). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences 54(3): 347-350.
  • Kaczorek, T. (2007a). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, JESA Journal, 2007, (submitted).
  • Kaczorek, T. (2007b). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4): 139-143.
  • Kaczorek, T. (2007c). Cone-realizations for multivariable continuous-me systems with delays, Advances in Systems Science and Applications 8(1): 25-34.
  • Kaczorek, T. (2007d). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367.
  • Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2):223-228.
  • Miller, K. S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.
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  • Oldham, K. B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
  • Ortigueira, M. D. (1997). Fractional discrete-time linear systems, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing 97, Munich, Germany, pp. 2241-2244.
  • Ostalczyk, P. (2000). The non-integer difference of the discretetime function and its application to the control system synthesis, International Journal of Systems Science 31(12): 1551-1561.
  • Ostalczyk, P. (2004). Fractional-order backward difference equivalent forms. Part I-Horner's form, Proceedings of the 1-st IFAC Workshop on Fractional Differentation and Its Applications, FDA'04, Enseirb, Bordeaux, France, pp. 342-347.
  • Ostalczyk, P. (2004). Fractional-order backward difference equivalent forms. Part II-Polynomial form, Proceedings of the 1-st IFAC Workshop on Fractional Differentation and Its Applications, FDA'04, Enseirb, Bordeaux, France, pp. 348-353.
  • Oustaloup, A. (1993). Commande CRONE, Hermès, Paris.
  • Oustaloup, A. (1995). La dèrivation non entière. Hermès, Paris.
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  • Podlubny, I., Dorcak, L. and Kostial, I. (1997). On fractional derivatives, fractional order systems and $PI^{λ}D^{μ}$-controllers, Proceedings of the 36-th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4985-4990.
  • Reyes-Melo, M.E., Martinez-Vega, J.J., Guerrero-Salazar C.A. and Ortiz-Mendez, U. (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., Retiére, N. and Ivanes, M. (2001). Turbine generator modeling by non-integer order systems, Proceedings of the IEEE International Conference on Electric Machines and Drives Conference, IEMDC 2001, Cambridge, MA, USA, pp. 185-187.
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  • Sjöberg, M. and Kari, L. (2002). Non-linear behavior of a rubber isolator system using fractional derivatives, Vehicle System Dynamics 37(3): 217-236.
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Bibliografia
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