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.
@article{bwmeta1.element.bwnjournal-article-amcv19i1p89bwm, author = {Tadeusz Kaczorek}, title = {Reachability of cone fractional continuous-time linear systems}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {19}, year = {2009}, pages = {89-93}, zbl = {1169.93004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p89bwm} }
Tadeusz Kaczorek. Reachability of cone fractional continuous-time linear systems. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) pp. 89-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p89bwm/
[000] Engheta, N. (1997). On the role of fractional calculus in electromagnetic theory, IEEE Transactions on Antennas and Propagation 39(4): 35-46.
[001] Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. | Zbl 0988.93002
[002] 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.
[003] Gałkowski, K. (2005). Fractional polynomials and nD systems. Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS'2005, Kobe, Japan, CD-ROM.
[004] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. | Zbl 1005.68175
[005] Kaczorek, T. (2006). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences 54(3): 347-350. | Zbl 1194.93129
[006] Kaczorek, T. (2007a). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, JESA Journal, 2007, (submitted).
[007] Kaczorek, T. (2007b). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4): 139-143.
[008] Kaczorek, T. (2007c). Cone-realizations for multivariable continuous-me systems with delays, Advances in Systems Science and Applications 8(1): 25-34.
[009] Kaczorek, T. (2007d). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367. | Zbl 1152.93393
[010] Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2):223-228. | Zbl 1235.34019
[011] Miller, K. S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY. | Zbl 0789.26002
[012] Nishimoto, K. (1984). Fractional Calculus, Decartess Press, Koriama. | Zbl 0605.26006
[013] Oldham, K. B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. | Zbl 0292.26011
[014] 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.
[015] 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. | Zbl 1080.93592
[016] 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.
[017] 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.
[018] Oustaloup, A. (1993). Commande CRONE, Hermès, Paris.
[019] Oustaloup, A. (1995). La dèrivation non entière. Hermès, Paris. | Zbl 0864.93004
[020] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. | Zbl 0924.34008
[021] Podlubny, I., Dorcak, L. and Kostial, I. (1997). On fractional derivatives, fractional order systems and -controllers, Proceedings of the 36-th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4985-4990.
[022] 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.
[023] 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.
[024] Samko, S. G., Kilbas, A.A. and Martichew, O.I. (1993). Fractional Integrals and Derivative. Theory and Applications, Gordon & Breac, London.
[025] Sierociuk, D. and Dzieliński, 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. | Zbl 1334.93172
[026] Sjöberg, M. and Kari, L. (2002). Non-linear behavior of a rubber isolator system using fractional derivatives, Vehicle System Dynamics 37(3): 217-236.
[027] 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.
[028] 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.
[029] 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.