Open Access

Fractional Positive Continuous-Time Linear Systems and Their Reachability

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Selected Topics in Biological Cybernetics (special section, pp. 117 - 170), Andrzej Kasiński and Filip Ponulak (Eds.)

Cite

Engheta N. (1997). On the role of fractional calculus in electromagnetic theory, IEEE Transactions on Atennas and Propagation 39(4): 35-46.10.1109/74.632994Search in Google Scholar

Farina L.and Rinaldi S. (2000). Positive Linear Systems, Theory and Applications, J. Wiley, New York.Search in Google Scholar

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

Gałkowski K. and Kummert A. (2005). Fractional polynomials and nD systems, Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS'2005, Kobe, Japan, CD-ROM.Search in Google Scholar

Kaczorek T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2Search in Google Scholar

Kaczorek T. (2006). Computation of realizations of discrete-time cone systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 54(3): 347-350.Search in Google Scholar

Kaczorek T. (2007a). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4), (in press).10.23919/ECC.2007.7068247Search in Google Scholar

Kaczorek T. (2007b). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367.10.23919/ECC.2007.7068247Search in Google Scholar

Klamka J. (2002). Positive controllability of positive dynamical systems, Proceedings of American Control Conference, ACC-2002, Anchorage, AL, CD-ROM.10.1109/ACC.2002.1025385Search in Google Scholar

Klamka J. (2005). Approximate constrained controllability of mechanical systems, Journal of Theoretical and Applied Mechanics 43(3): 539-554.Search in Google Scholar

Miller K.S. and B. Ross (1993). An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Willey, New York.Search in Google Scholar

Moshrefi-Torbati M. and K. Hammond (1998). Physical and geometrical interpretation of fractional operators, Journal of the Franklin Institute335B(6): 1077-1086.10.1016/S0016-0032(97)00048-3Search in Google Scholar

Nishimoto K. (1984). Fractional Calculus, Koriyama: Decartes Press.Search in Google Scholar

Oldham K.B. and J. Spanier (1974). The Fractional Calculus, New York: Academic Press.Search in Google Scholar

Ortigueira M.D. (1997). Fractional discrete-time linear systems, Procedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Munich, Germany, Vol. 3, pp. 2241-2244.Search in Google Scholar

Ostalczyk P. (2000). The non-integer difference of the discrete-time function and its application to the control system synthesis, International Journal of Systems Science 31(12): 1551-1561.10.1080/00207720050217322Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

Oustalup A. (1993). Commande CRONE, Paris, Hermès.Search in Google Scholar

Oustalup A. (1995). La dérivation non entiére, Paris: Hermès.Search in Google Scholar

Podlubny I. (1999). Fractional Differential Equations, San Diego: Academic Press.Search in Google Scholar

Podlubny I. (2002). Geometric and physical interpretation of fractional integration and fractional differentation, Fractional Calculs and Applied Analysis 5(4): 367-386.Search in Google Scholar

Podlubny I., L. Dorcak and I. Kostial (1997). On fractional derivatives, fractional order systems and PIλDμ-controllers, Procedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4985-4990.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

Samko S. G., A.A. Kilbas and O.I. Marichev (1993). Fractional Integrals and Derivatives. Theory and Applications. London: Gordon and Breach.Search in Google Scholar

Sierociuk D. and D. Dzieliński (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.Search in Google Scholar

Sjöberg M. and L. Kari (2002). Non-linear behavior of a rubber isolator system using fractional derivatives, Vehicle System Dynamics 37(3): 217-236.10.1076/vesd.37.3.217.3532Search in Google Scholar

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

Vinagre M. and V. Feliu (2002) Modeling and control of dynamic systems using fractional calculus: Application to electrochemical processes and flexible structures, Proceedings of the 41st IEEE Conference Decision and Control, Las Vegas, NV, USA, pp. 214-239.Search in Google Scholar

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

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics