Reachability of cone fractional continuous-time linear systems
International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 89-93.

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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.
Keywords: cone fractional system, linear system, reachability
Mots-clés : system ułamkowy, system liniowy, osiągalność
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Kaczorek, T. Reachability of cone fractional continuous-time linear systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 1, pp. 89-93. http://geodesic.mathdoc.fr/item/IJAMCS_2009_19_1_a7/

[1] Engheta, N. (1997). On the role of fractional calculus in electromagnetic theory, IEEE Transactions on Antennas and Propagation 39(4): 35-46.

[2] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.

[3] Ferreira, N.M.F. and Machado, J.A.T. (2003). Fractional-order hybrid control of robotic manipulators, Proceedings of the 11-th International Conference on Advanced Robotics, ICAR'2003, Coimbra, Portugal, pp. 393-398.

[4] Gałkowski, K. (2005). Fractional polynomials and nD systems. Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS'2005, Kobe, Japan, CD-ROM.

[5] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.

[6] Kaczorek, T. (2006). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences 54(3): 347-350.

[7] Kaczorek, T. (2007a). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, JESA Journal, 2007, (submitted).

[8] Kaczorek, T. (2007b). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4): 139-143.

[9] Kaczorek, T. (2007c). Cone-realizations for multivariable continuous-me systems with delays, Advances in Systems Science and Applications 8(1): 25-34.

[10] Kaczorek, T. (2007d). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367.

[11] Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2):223-228.

[12] Miller, K. S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY.

[13] Nishimoto, K. (1984). Fractional Calculus, Decartess Press, Koriama.

[14] Oldham, K. B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.

[15] 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.

[16] 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.

[17] 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.

[18] 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.

[19] Oustaloup, A. (1993). Commande CRONE, Hermès, Paris.

[20] Oustaloup, A. (1995). La dèrivation non entière. Hermès, Paris.

[21] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.

[22] Podlubny, I., Dorcak, L. and Kostial, I. (1997). On fractional derivatives, fractional order systems and PIλDμ-controllers, Proceedings of the 36-th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4985-4990.

[23] 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.

[24] 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.

[25] Samko, S. G., Kilbas, A.A. and Martichew, O.I. (1993). Fractional Integrals and Derivative. Theory and Applications, Gordon Breac, London.

[26] Sierociuk, D. and Dzieli´nski, D. (2006). Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, International Journal of Applied Mathematics and Computer Science 16(1): 129-140.

[27] Sjöberg, M. and Kari, L. (2002). Non-linear behavior of a rubber isolator system using fractional derivatives, Vehicle System Dynamics 37(3): 217-236.

[28] Vinagre, B. M., Monje, C. A. and Calderon, A.J. (2002). Fractional order systems and fractional order control actions, Lecture 3 IEEE CDC'02 TW#2: Fractional Calculus Applications in Automatic Control and Robotics.

[29] Vinagre, B. M. and Feliu, V. (2002). Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures, Proceedings of the 41-st IEEE Conference on Decision and Control, Las Vegas, NV, USA, pp. 214-239.

[30] Zaborowsky, V. and Meylaov, R. (2001). Informational network traffic model based on fractional calculus, Proceedings of International Conference on Info-tech and Info-net, ICII 2001, Beijing, China, Vol. 1, pp. 58-63.