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Realization problem for fractional continuous-time systems

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Języki publikacji
EN
Abstrakty
EN
The realization problem for positive fractional continuous-time linear systems is addressed. Sufficient conditions for the existence of positive realizations for continuous-time linear systems are established. Procedures for computation of positive fractional realizations for SISO and MIMO continuous-time linear systems are proposed and illustrated by numerical examples.
Rocznik
Strony
43--58
Opis fizyczny
Bibliogr. 33 poz., wzory
Twórcy
autor
  • Bialystok Technical University, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland, kaczorek@isep.pw.edu.pl
Bibliografia
  • [1] N. ENGHETA: On the role of fractional calculus in electromagnetic theory. IEEE Trans. Atenn. Prop., 39(4), 1997, 35-46.
  • [2] L. FARINA and S. RINALDI: Positive linear systems. Theory and applications. J. Wiley, New York, 2000.
  • [3] N. M. F. FERREIRA and J. A. T. MACHADO: Fractional-order hybrid control of robotic manipulators. Proc. I I th Int. Conf. Advanced Robotics, Coimbra, Portugal, (2003), 393-398.
  • [4] K. GAŁKOWSKI and A KUMMERT: Fractional polynomials and nD systems. Proc IEEE Int. Symp. Circuits and Systems, Kobe, Japan, (2005), CD-ROM.
  • [5] T. KACZOREK: Positive 1D and 2D systems. Springer-Verlag, London, 2002.
  • [6] T. KACZOREK: Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn., 54(3), (2006), 347-350.
  • [7] T. KACZOREK: Reachability and controllability to zero tests for standard and positive fractional discrete-time systems. J. European System Engn., (2008), in press.
  • [8] T. KACZOREK: Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6(4), (2007).
  • [9] T. KACZOREK: Reachanbility and controllability to zero of cone fractional linear systems. Archives of Control Scienes, 17(3), (2007), 357-367.
  • [10] T. KACZOREK: Realization problem for positive continuous-time systems with delays. Intern. J. Comput. Intellig. and Appl., 6(2), (2006), 289-298.
  • [11] T. KACZOREK: Realization problem for singular positive continuous-time systems with delays. Control and Cybernetics, 36(1), (2007), 2-11.
  • [12] T. KACZOREK: Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comp. Sci., 18(1), (2008), (in press).
  • [13] K. S. MILLER and B. Ross: An Introduction to the fractional calculus and fractional differenctial equations. Willey, New York 1993.
  • [14] M. MOSHREFI-TORBATI and K. HAMMOND: Physical and geometrical interpretation of fractional operators. J. Franklin Inst. 335B(6), (1998), 1077-1086.
  • [15] K. NISHIMOTO: Fractional calculus. Koriama: Decartess Press, 1984.
  • [16] K. B. OLDHAM and J. SPANIER: The fractional calculus. New York: Academmic Press, 1974.
  • [17] M. D. ORTIGUEIRA: Fractional discrete-time linear systems. Proc. IEE-ICASSP 97, Munich, Germany, 3, (1997), 2241-2244.
  • [18] P. OSTALCZYK: The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J Syst, Sci. 31(12), (2000), 1551-1561.
  • [19] P. OSTALCZYK: Fractional-order backward difference equivalent forms. Part I -Horner's form. Proc. 1-st IFAC Workshop Fractional Differentation and its Applications, Enseirb, Bordeaux, France, (2004), 342-347.
  • [20] P. OSTALCZYK: Fractional-order backward difference equivalent forms. Part II -Polynomial form. Proc. 1st IFAC Workshop Fractional Differentation and its Applications, Enseirb, Bordeaux, France, (2004), 348-353.
  • [21] A. OUSTALUP: Commande CRONE. Paris, Hermes, 1993.
  • [22] A. OUSTALUP: La derivation non entiere. Paris: Hermes, 1995.
  • [23] I. PODLUBNY: Fractional differential equations. San Diego: Academic Press, 1999.
  • [24] I. PODLUBNY: Geometric and physical interpretation of fractional integration and fractional differentation. Fract. Cale. Appl. Anal. 5(4), (2002), 367-386.
  • [25] I. PODLUBNY, L. DORCAK and I. KOSTIAL: On fractional derivatives, fractional order systems and PI xDP-controllers. Proc. 36th IEEE Conf. Decision and Control, San Diego, CA, (1997), 4985-4990.
  • [26] M. E. REYES-MELO, J. J. MARTINEZ-VEGA, C. A. GUERRERO-SALAZAR and U. ORTIZ-MENDEZ: Modelling and relaxation phenomena in organic dielectric materials. Application of differential and integral operators of fractional order. I Optoel. Adv. Mat., 6(3), (2004), 1037-1043.
  • [27] D. RIU, N. RETIERE and M. IVANES: Turbine generator modeling by non-integer order systems. Proc. IEEE Int. Electric Machines and Drives Conf, Cambridge, MA, (2001), 185-187.
  • [28] S. G. SAMKO, A. A. KILBAS and O. I. MARTICHEW: Fractional integrals and derivative. Theory and Applications. London, Gordon&Breac, 1993.
  • [29] D. SIEROCIUK and D. DZIELIŃSKI: Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation. Int. J. Appl. Math. Comp. Sci., 16(1), (2006), 129-140.
  • [30] M. SJÖBERG and L. KARI: Non-linear behavior of a rubber isolator system using fractional derivatives. Vehicle Syst. Dynam., 37(3), (2002), 217-236.
  • [31] B. M. VINAGRE, C. A. MONJE and A.J. CALDERON: Fractional order systems and fractional order control actions. Lecture 3 IEEE CDC'02 TW#2: Fractional calculus Applications in Autiomatic Control and Robotics.
  • [32] B. M. VINAGRE and V. FELIU: Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures. Proc. 41st IEEE Conf Decision and Control, Las Vegas, NV, (2002), 214-239.
  • [33] V. ZABOROWSKY and R. MEYLAOV: Informational network traffic model based on fractional calculus. Proc. Mt. Conf Info-tech and Info-net, Beijing, China, 1 (2001), 58-63.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0045-0003
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