A note on the controllability and the observability of fractional dynamical systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 2, Issue PART 1, 2006, Pages 493-498

  Bettayeb, Maamar ^a   Djennoune, Said ^b  

^a UNIVERSITY OF SHARJAH   (United Arab Emirates)

^b UNIVERSITÉ MOULOUD MAMMERI   (Algeria)

Author keywords

Controllability; Fractional order systems; Lyapunov equation; Observability

Indexed keywords

ALGEBRA; APPLICATION PROGRAMS; DYNAMICAL SYSTEMS; LINEAR CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; OBSERVABILITY;

CONTROLLABILITY GRAMIANS; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL; FRACTIONAL DYNAMICAL SYSTEMS; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LINEAR DYNAMICAL SYSTEMS; LYAPUNOV EQUATION;

CONTROLLABILITY;

EID: 79961111422     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20060719-3-pt-4902.00082     Document Type: Conference Paper

References (32)

1. Arena, P., Caponetto, R., Fortuna, L., and Porto, D., 2000, Nonlinear noninteger order circuits and systems- An introduction., World Scientific on Nonlinear Science, 38.
2. Axtell, M., and Bise, E. M., 1990, Fractional calculus applications in control systems, In Proceedings of the IEEE Nat.Aerospace and Electronics Conference, New-York, pp. 563-566.
3. Battaglia, J. L., Cois, O., Puigsegur, L., and Oustaloup, A., 2001, Solving an inverse heat conduction problem using a non-integer identified model, International Journal of Heat and mass Transfer, 44.
4. Chen, H. Q., Ahn, H. and Podlubny, I., 2005a, Robust stability check of fractional order linear time invariant systems with interval uncertainties, The 2005 International Conference on Mechatronics and Automation, Niagara Falls, Ontario, Canada, July 29 - August 1, pp. 210-215. (Pubitemid 41594561)
5. Chen, H. Q., Ahn, H. and Xue, D., 2005b, Robust controllability of interval fractional order linear time invariant systems, The 2005 ASME 2005 Long Beach, ASME-DETC/VIB 2005: 2nd Symposium on Fractional Derivatives and their Applications.
6. Chen, C. T., 1984, Linear system theory and design, Holt, Rinehart andWiston, New-York.
7. Cois, O., 2002, Systèmes linéaires non entiers et identification par modèle non entier: application en thermique, PhD Thesis, Université de Bordeaux I, France.
8. Dorcak, L., Petras, I., and Kostial, I., 2000, Modeling and analysis of fractional-order regulated systems in the state space, In Proc. of ICCC'2000, High Tatras, Slovak Republic, pp 185-188.
9. Fonseca Ferreira, N. M., Tenreiro Machado, J. A., Galhana, A. M. and Cunha, J. B., 2004, Fractionalorder position/force robot control, IFAC Workshop on Fractional Differentiation and its Applications, FDA'04, Bordeaux, France.
10. Gorenflo, R., and Mainardi, F., 2000, Fractional calculus, integral and differential equations of fractional order, CISM Lectures Notes, International Center of Mechanical Sciences, Udine, Italy.
11. Hanyga, A., 2003, Internal variable models of viscoelasticity with fractional relaxatioon laws, in Proc. of DETC 2003/VIB, 48395, ASME.
12. Hotzel R., and Fliess, M., 1998, On linear system with a fractional derivation: introductory theory and examples, Mathematics and Computers in Simulation, 45, pp 385-395.
13. 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, 13, 253-265.
14. Manabe, S., 1963, The system design by the use of a model consisting of a saturation and non-integer integrals, ETJ of Japan, 8(3-4, pp. 147-150.
15. Lin, J. Poinot, T., Trigeassou, J.C., Kabbaj, H., and Faucher, J., 2000, Modélisation et identification d'ordre non entier d'une machine asynchrone, CIFA'2000, Confé Internationale Francophone d'Automatique, Lille, France.
16. Matignon, D., 1994, Représentation en variables d'état de modèles de guides d'ondes avec dérivation fractionnaire, PhD Thesis, Univeristé of Paris Sud, Orsay, France.
17. Matignon, D. d'Andréa Novel, B., Depalle, P. and Oustaloup, A., 1994, Viscothermal losses in wind instrument: a non integer model, Academic Verlag Edition.
18. Matignon, D., 1996, Stability results on fractional differential with application to control processing, In IAMCS, IEEE SMC Proceedings Conference, Lille, France, pp. 963-968.
19. Matignon, D., and d'Andréa-Novel, B., 1996, Some results on controllability and observability of finitedimensional fractional differential systems, In IMACS, IEEE-SMC Proceedings Conference, Lille, France, pp. 952-956.
20. Matignon, D., and d'Andréa-Novel, B., 1997, Observer-based controllers for fractional differential systems, In Proceedings of the IEEE Conference on Decision and control, San Diego.
21. Miller, K. S., and Ross, B., 1993, An introduction to the fractional calculus and fractional differential equations, 1993,Wiley, New-York.
22. Mittag-Leffler, G., 1904, Sur la representation analytique d'une branche uniforme d'une fonction monogene, Acta Mathematica, 29, pp 10-181.
23. Oldham, K. B., and Spanier, J., 1974, The fractional calculus, Academic Press, New-York.
24. Oustaloup, A., 1983, Systèmes asservis linéaires d'ordre fractionnaire, Masson Edition.
25. Oustaloup, A., 1995, La dérivation non entière: théorie, synthèse et applications, Hermes Edition, Paris, France.
26. Petras, I., 2000, Control of fractional-order Chua's system, Journal of Circuit, Systems and Computer, pp. 1-5.
27. Podlubny, I., 1999, Fractional differential equations, Academic press, San Diego, U. S. A.
28. Raynaud, H. F., and Zergainoh, A., 2000, Statespace representation for fractional order controllers, Automatica, 36, pp 1017-1021.
29. Sabatier, J., Cois O., and Oustaloup, A., 2002, Commande de systèmes non entiers par placement de pôles, Deuxième Conférence Internationale Francophone d'Automatique, CIFA, Nantes, France.
30. Samko, S. G., Kilbas, A. A., and Marichev, O. I., 1993, Fractional integrals and derivatives: theory and applications, Gordon and Breach Science Publisher, Amsterdam.
31. Valerio, D., and Sa da Costa, J., 2004, Non integer order control of a flexible robot, IFAC Workshop on Fractional Differentiation and its Applications, FDA'04, Bordeaux, France.
32. 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.