PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2008 | 18 | 2 | 213-222
Tytuł artykułu

Controllability and observability of linear discrete-time fractional-order systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.
Rocznik
Tom
18
Numer
2
Strony
213-222
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-06-17
poprawiono
2007-10-21
Twórcy
autor
  • Laboratoire de Conception et Conduite des Systèmes de Production, Universitè Mouloud Mammeri de Tizi-Ouzou, BP 17 RP, Tizi-Ouzou, Algeria
  • Laboratoire de Conception et Conduite des Systèmes de Production, Universitè Mouloud Mammeri de Tizi-Ouzou, BP 17 RP, Tizi-Ouzou, Algeria
  • Electrical & Computer Engineering Department, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
Bibliografia
  • Antsaklis P.J. and Michel A.N. (1997). Linear Systems, McGraw-Hill, New York.
  • Åström K. J. and Wittenmark B. (1996). Computer-Controlled Systems, Theory and Design, 3rd Ed., Prentice Hall Inc., New Jersey.
  • Axtell M. and Bise E. M. (1990). Fractional calculus applications in control systems, Proceedings of the IEEE 1990 National Aerospace and Electronics Conference, New York, USA, pp. 536-566.
  • Battaglia J. L., Cois O., Puigsegur L. and Oustaloup A. (2001). Solving an inverse heat conduction problem using a noninteger identified model, International Journal of Heat and Mass Transfer, 44(14): 2671-2680.
  • Bettayeb M. and Djennoune S. (2006). A note on the controllability and the observability of fractional dynamical systems, Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Workshop Applications, Porto, Portugal, pp. 506-511.
  • Boukas E.K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability, Mathematical Problems in Engineering, bf 2006 (ID42489): 1-10.
  • Cois O., Oustaloup A., Battaglia E. and Battaglia J.L. (2002). Non integer model from modal decomposition for time domain identification, 41st IEEE CDC'2002 Tutorial Workshop 2, Las Vegas, USA.
  • Debeljković D. Lj., Aleksendrić M., Yi-Yong N. and Zhang Q. L. (2002). Lyapunov and non-Lyapunov stability of linear discrete time delay systems, Facta Universitatis, Series: Mechanical Engineering 1(9): 1147-1160.
  • Dorčák L., Petras I. and Kostial I. (2000). Modeling and analysis of fractional-order regulated systems in the state-space, Procedings of International Carpathian Control Conference, High Tatras, Slovak Republic, pp. 185-188.
  • Dzieliński A. and Sierociuk D. (2005). Adaptive feedback control of fractional order discrete state-space systems, Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation, and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'05), Vienna Austria, pp. 804-809.
  • Dzieliński A. and Sierociuk D. (2006). Observer for discrete fractional order systems, Proceedings of the 2nd IFAC Workshop on Fractional Differentiation Applications, Porto, Portugal, pp. 524-529.
  • Dzieliński A. and Sierociuk D. (2007). Reachability, controllability and observability of the fractional order discrete statespace system, Proceedings of the IEEE/IFAC International Conference on Methods and Models in Automation and Robotics, MMAR'2007, Szczecin, Poland, pp. 129-134.
  • Gorenflo R. and Mainardi F. (1997). Fractional calculus: Integral and differential equations of fractional order, in (A. Carpintieri and F. Mainardi, Eds.) Fractals and Fractional Calculus in Continuum Mechanics, Vienna, New York, Springer Verlag.
  • Hanyga A. (2003). Internal variable models of viscoelasticity with fractional relaxation laws, Proceddings of Design Engineering Technical Conference, Mechanical Vibration and Noise, 48395, American Society of Mechanical Engineers, Chicago, USA.
  • Hotzel R. and Fliess M.(1998). On linear system with a fractional derivation: Introductory theory and examples, Mathematics and Computers in Simulation 45 (3): 385-395.
  • Ichise M., Nagayanagi Y. and Kojima T. (1971). An analog simulation of non integer order transfer functions for analysis of electrode processes, Journal of Electroanalytical Chemistry 33(2): 253-265.
  • Kilbas A. A., Srivasta H. M. and Trujillo J. J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
  • Lakshmikantham D. T. V. (1998). Theory of Difference Equations: Numerical Methods and Applications, Academic Press, New York.
  • Manabe S. (1960). The non-integer integral and its application to control systems, Japanese Institute of Electrical Engineers Journal 80(860): 589-597.
  • Matignon D. (1994). Reprèsentation en variables d'ètat de modèles de guides d'ondes avec dèrivation fractionnaire, Ph.D. thesis, Universitè Paris XI, France.
  • Matignon D., d'Andrèa Novel B., Depalle P. and Oustaloup A. (1994). Viscothermal Losses in Wind Instruments: A NonInteger Model, Academic Verlag, Berlin.
  • Matignon D. and d'Andrèa-Novel B. (1996). Some results on controllability and observability of finite-dimensional fractional differential systems, Proceedings of the IMACS, IEEE SMC Conference, Lille, France, pp. 952-956.
  • Matignon D. (1996). Stability results on fractional differential with application to control processing, Proceedings of the IAMCS, IEEE SMC Conference, Lille, France, pp. 963968.
  • Miller K. S. and Ross B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
  • Mittag-Leffler G. (1904). Sur la reprèsentation analytique d'une branche uniforme d'une fonction monogène, Acta Mathematica 29: 10-181.
  • Oldham K. B. and Spanier J. (1974). The Fractional Calculus, Academic Press, New York.
  • Oustaloup A. (1983). Systèmes asservis linèaires d'ordre fractionnaire, Masson, Paris.
  • Oustaloup A. (1995). La Dèrivation non entière: Thèorie, synthèse et applications, Hermès, Paris.
  • Podlubny I. (1999). Fractional Differential Equations, Academic Press, San Diego.
  • Peng Y., Guangming X. and Long W. (2003). Controllability of linear discrete-time systems with time-delay in state, available at dean.pku.edu.cn/bksky/1999tzlwj/4.pdf.
  • Raynaud H. F., Zergainoh, A. (2000). State-space representation for fractional-order controllers, Automatica 36(7): 10171021.
  • Sabatier J., Cois O. and Oustaloup A. (2002). Commande de systèmes non entiers par placement de pôles, Deuxième Confèrence Internationale Francophone d'Automatique, CIFA, Nantes, France.
  • Samko S. G., Kilbas A. A. and Marichev O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Amsterdam.
  • Sierociuk D. and Dzieliński A. (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.
  • Valerio D. and Sa da Costa J. (2004). Non-integer order control of a flexible robot, Proceedings of the IFAC Workshop on Fractional Differentiation and its Applications, FDA'04, Bordeaux, France.
  • Vinagre B. M., Monje C. A. and Caldero A. J. (2002). Fractional order systems and fractional order actions, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics, 41st IEEE CDC, Las Vegas, USA.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv18i2p213bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.