Reachability of cone fractional continuous-time linear systems

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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. Zbl0988.93002
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. Zbl1005.68175
6. Kaczorek, T. (2006). Computation of realizations of discretetime cone systems, Bulletin of the Polish Academy of Sciences 54(3): 347-350. Zbl1194.93129
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. Zbl1152.93393
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. Zbl1235.34019
12. Miller, K. S. and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY. Zbl0789.26002
13. Nishimoto, K. (1984). Fractional Calculus, Decartess Press, Koriama. Zbl0605.26006
14. Oldham, K. B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. Zbl0292.26011
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. Zbl1080.93592
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. Zbl0864.93004
21. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA. Zbl0924.34008
22. Podlubny, I., Dorcak, L. and Kostial, I. (1997). On fractional derivatives, fractional order systems and $P{I}^{\lambda }{D}^{\mu }$-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 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. Zbl1334.93172
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. 

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