[1] Ait Messaoud L. (2007)Contibution à la commande
dessystèmespar des régulateurs d'ordre non entierApplication
àla commande deamachine asynchrone. Mémoire de Magister,
Univeristé Mouloud Mammeri de Tizi-Ouzou.
[2] Aoun M. (2005). Systèmes linéaires nonentiers
et identi~cation par bases orthogonales non entières. Phd Thesis,
Université de Bordeaux 1
[3] Al-Alaoui M.A. (1993). Novel digital integrator
anddi~erentiator.Electronics letters, vol. 29, n 4, pp. 376-378.
[4] Baker J.E. (1987). Adaptative selection methods forgenetics
algorithms.J.J. Creffenstette (Ed.) lst International conference on genetic
algorithmsnd their applications. pp. 14-21, New Jersey.
[5] Barret P. (1982) Régimes transitoires des
machinestournantes électriiues. Editions Eyrolles, Paris.
[6] Bettayeb M., Silverman L.Met Safonov M.G (1980). Optimal
approximation of continuous-time systems. 2Oth IEEE Conference on Decision and
Control CDC''8, 21-24 December, Albuquerque New Mexicopp10-12.
[7] Bettayeb M. et Djennoune S. (2006) A Note on the
Controllability and theObservability of Fractional Dynamical Systems. In :
Proceedings of the 2th IFAC Workshop on Fractional Di~erentiation and
itsApplications, Porto, Portugal.
[8] Blaschke F. (1972), The principle offield orientation as
appliedohe nee transsektor closed-loop control systemforrotating ~eldmachines.
Siemens Review n. 34, pp. 217- 220.
[9] Caputo M. (1967). Linear models ofdissipation whoseq is
almost frequency independent. Ceopthysical journal of tthe royal astronomical
society. vol. 2, n 13, pp. 529-539.
[10] Carlson G.E. et Halijak CA. (1964) Approximationof
fractional capacitor(1/s)1/n by a regular Newton
ProcessIRE Transactions on circuit ttheory. vol. 2, pp. 210-213.
[11] Charef A. et Sun H.H. (1990)Time domain analysis of
fractal system.nEngeneering in Medicine and
BiologysocietyyProceedings ofthe12th Annual international
Conference oftthe IEEE, n 18, pp. 597-621.
[12] Charef A., Sun H.H., Tsao Y.Y. et Onaral BFractal system
as representedby singularity function. IEEE Transactions on Automatic Control .
vol. 37, n 9, pp. 1465-1470
[13] Charef A. (2006)Modeling and analogrealizationof the
fundamentalinearractional order differential equation. Nonlinear Dynamics, vol.
46, pp.195-210.
[14] Chen C.T. (1984). Linear system ttheory and design. Holt,
Rinehart and Wiston New-York.
[15] Chen Y.Q. et Moore K.L. (2002) DiscretizationSchemes
forFractional-Order Differentiators and Integrators. IEEE Transactions on
Circuits and Systems-IFundamental Ttheory and Applications , 49(3), pp.
363-367
[16] Clerc M. (2005). L'Optimisation par essaims particulaires,
Versions paramétriques et adaptatives, Editions Hermès, Paris.
[17] Cole K. S. et Cole R.H. (1941) Dispersion and absorption n
dielectrics, alternation current characterization. Journal of Cthemical
Pthysics, vol. 9, pp. 1417-1418
[18] Davidson D. et Cole R. (1950) Dielectric relaxation n
glycerine.Journal of Cthemistry and Pthysics. vol. 18, pp. 1417-1418.
[19] De Larminat P. (1996) Automatique : Commande des
systèmes inéaires. Editions Hermès, Paris.
[20] Djamah T. et Mansouri R. (2006) Développement
d'une nouvelleméthode de calcul d'un modèle d'état
à partir dun modèle transfertd'ordrenon entiermonovariable.
rapport interne.
[21] Dzielinski A. et Sierociuk D. (2006) Stability of
Discrete FractionalOrder StateSpace Systems. Proceedings of the 2nd IFAC
Workshop onFractionalDi~erentiation and its Applications Porto, Portugal.
[22] Glover K. (1984)All optimal Hankel-norm approximations
ofinearmultivariable systems and their H8-error bounds.
International Journal of Control , vol. 39, pp. 1115-1193.
[23] Goldberg D.E. (1989) Cenetic algorithmsin search,
optimiiation, and machineearr ning. Addison-Wesley, New York.
[24] Gorenflo R. (1997)Fractional calculus Some
numericalmethods. In : A. Carpinteri and F. Mainardi (eds.). Fractals and
Fractional Calculus n ContinuumMechanics. Springer Verlag, Vienna, New York
[25] Guglielmi M., (2002). Approximation optimale
duntransfertnon entierpar un réseau de cellules. In : Proceedings de la
Conférence InternationaleFrancophone ddAutomaa tique, Nantes French,
8-10 julypp534-539
[26] Grunwald A.K. (1867)Ueber begrenzte derivationen und deren
anwendung. Z. Angew. Math. Phys.. n 12, pp. 441-480.
[27] Gustavsen B. et Semlyen A(1999) Rational approximation of
freeuency domain responses by vector fittingIEEE trans. Power Delivery. vol.
14, pp. 1052-1061
[28] Gustavsen B. (2004)A robust approach for system
denti~cationn the freeuency domain. IEEE trans. Power Delivery. vol. 19, n 3,
pp. 1167-1173
[29] Haupt R.L. and Haupt S.E. (1998) Practical Cenetic
Algorithm. John Wiley & Sons, Yew York.
[30] Héliea T., Matignon D. (2006) Representations
with polesand cuts forheimedomain simulation of fractional systems
andirrationaltransfer functions.Signal Processing vol. 86, pp. 2516-2528
[31] Hotzel R. (1998)Contribution à la théorie
structurelle et àa commande des systtmes linéaires
fractionnaires, PhD. Thesis, Université de Paris SudOrsay
[32] Kavranoglu D. et Bettayerb M. (1993) Characterization of
theolution to the optimal H model reduction prorblem. S ystems and Control
Letters, vol. 20, pp. 99-107.
[33] Kennedy J. and Erberhart R. (1995) Particle
SwarmOptimization.IEEE International Conference Neural Networks, vol. IV, pp.
1942-1948 PerthAustralia.
[34] Kilrbas A.A., Srivastava H.Met Trujillo JJ (2006) Theor y
and applications offractional di~eretial equations. Elsevier, North-Holland.
[35] Levy E. (1959). Complex curve fitting.IRE transactions on
automaticcontrol , 4, pp. 37-43.
[36] Liouville J. (1832). Mémoire sur quelques
questions de géométrie et demécnique, et sur un nouveau
genre de calcul pour résoudre ces équations.l'Ecole Pol
ytechnique, vol. 13, pp. 71-162.
[37] Lorenzo C.F. et Hartley TT (1998) Initialization,
conceptualization, and application in the generalized fractional
calculus.NASA/TM 1998-208415, Springfield (VA) . NTIS.
[38] Lorenzo C. et Hartley T(2000) Initialized
FractionalCalculus.NASA TP-2000- 209943, Springfield (VA) NTIS.
[39] Loverro A. (2004) Fractional calculus History,deefinition
and applicationorhe engineer.
[40] Lurbich C. (1986). Discretized fractional calculus.SIAM
Journal of Mathematical Anal ysis, vol. 17, n 3, pp. 704-719.
[41] Liu Y. et Anderson B.D.O. (1989) Singular perturrbation
approximation of rbalanced systems. International Journal of Control , vol. 50,
pp. 1379-1405
[42] MacDonald J.R. (1987) Impedance spectroscop y. John Wiley,
New York.
[43] Tenreiro Machado J.A. (2001) Discrete-time fractional-order
controllers.Fractional Calculus Applied Anal ysis vol. 1, pp. 47-66.
[45] De Madrid A.P., Mafioso C. et HernÉindez R.
(2006) NewDirectDiscretization of the Fractional-Order
Differentiator/Integratorby the Chebyshev-PadéApproximation. In :
Proceedings of the 2nd IFA C Workshop onFractionalDi~erentiationndts
Applications, july 19-21 Porto .
[46] Magin R.L. (2006)Fractional Calculusin Bioengineering ,
Begell House Punlishers, Inc., Connecticut.
[47] Mansouri R., Bettayeb MDjamah Tet
DjennouneS.(2007).System dentiication in frequency domain by fractional Vector
Fitting algorithm.In Proc. of the second International Conference on Modeling
and Simulation ICMSAOO00. March 24-27, Abu Dhabi , UAE.
[48] Mansouri R., Bettayeb Met Djennoune S. (2008). State
SpaceFractionalModel Approximation Using Integral Representation.Soumis au
3ème IFAC Workshop on Fractional Di~erentiation and itsApplications,
00-00Novembre 2008, Ankara.
[49] Mansouri R., Bettayeb Met Djennoune S. (2009). State
Space fractionalModel Approximation by taking account of the initial
conditions.Submited to the third International Conference on Modeling and
Simulation ICMSAOO00. January 20-22, Sharjah, UAE.
[50] Marquardt D.W. (1963) An algorithm for east squares
estimation of non-linear parameters. Journal of the Society for Industrial and
AppliedMathematics, vol. 11, n 2, pp. 431-441.
[51] Matignon D. et Andréa-Novel B (1996) Some results
on controllability and observability of finite-dimensional fractional
di~erential systems.In IMACS, IEEE-SMC Proceedings Conference. pp. 952-956,
Lille, France
[52] Matignon D. (1998)Stability properties for generalized
fractional diierentialystems. In Proc. of the colloquium FDS''98Fractional
di~erentialystemsModels, Methods and Applications, n 5, pp. 145-158, Paris.
[53] Matignon D. (1998)Représentations en
variablesd'état demodèles de guides ddondes avec
dérivation fractionnaire . PhD Thesis, Université de
Paris-SudOrsay
[54] Matsuda K. et Fujii H. (1993) Optimised Wave Absorbing
ControlAnalytical and Experimental Results. Journal guidance control and
dynamics. vol.16, n6, pp.1146- 1153.
[55] Mbodje B. et Montseny G. (1995) Boundary
fractionalderivative control of the wave equation. IEEE Transaction on
Automatique Control . vol. 40 n 2, pp. 378-382
[56] Miller K.S. et Ross B. (1974) An introduction to
thefractional calculus and fractional differential equations. A Wiley
Interscience Publication
[57] Mittag-Leffler G. (1904) Sur lareprrsentationanalytique
d'une branche uniforme d'une fonction monogène. Acta Mathematica. n 29,
pp. 10-181
[58] Moore B. C. (1981)Principal component analysisn inear
systems Controllability, Observability and model reductionIEEE Transactions on
Automatic Control , vol. A C-26, pp. 17-31.
[59] Oldham K.B. et Spanier J. (1974) The fractional calculus.
Academic Press, New York and London.
[60] Onaral B. et Schwan H.P. (1982) Linear and
nonlinearproperties of platinum elec trode polarization, Part IFrequency
dependence at very ow frequencies.Med. Biol. Eng. Comput., vol. 20, pp.
299-306.
[61] Orjuela R., Malti R. Moze Met OustaloupA.(2006). Prise
en compte des conditions initiales lors de la simulation de fonctions
detransfertnon entières.In : Proceedings de la Conférence
Internationale Francophone ddAutomatique CIFA 20066 0,33 mai et ler juin 2006
Bordeaux.
[62] Ortigueira M.D. et Serralheiro A.J (2006) A new
east-squares approacho diierintegration ModellingSpecial Section : Fractional
CalculusApplicationsn Signals and Systems. vol. 10 pp.2582-2591.
[63] Ortigueira M., Valerio DSo Da CostaJ (2007). Identifying
a transfer function from a frequency response. In : Proceedings of the 6th
InternationalConference onMull tibody Systems, Nonlinear Dynamics andControl.
MSND C-14-3, ASME IDET C'07 September 4-7, Las VegasNevada, USA.
[64] Oustaloup A. (1983) Systèmes
asservislinéaires d'ordrefractionnaire. Editions Masson, Paris.
[65] Oustaloup A. (1995)La Dérivation non Entière
Théorie, synthèse et application, Editions Hermes, Paris.
[66] Ostalczyk P. (2003)Fundamental properties of the
fractional-order discrete-time integrator. Signal Processing n 83,
2367-2376.
[67] Podlubny I. (1999) Fractional di~erential equations .
Academic Press, San Diego
[68] Podlubny I. (2002). Geometric and physical
interpretation of fractionalntegration and fractional differentiation. Journal
offractional calculs and applied analysis. vol. 5, n 4, pp. 367-386.
[69] Podlubny I., PetrÉ I., Vinagre BMOLeary Pet
DorrÉk L 2002).Analogue realizations of fractional-order controllers.Non
linear Dynamics, vol. 29, pp. 281- 296.
[70] Poinot T. Trigeassou JC(2003) A method for modellingand
simulation of fractional systems. Signal Processing, vol. 83, pp. 2319-2333.
[71] Raynaud H.F. et Zergaïnoh A. (2000) State-space
representation for fractional order controllers, Automatica. n 36, pp.
1017-1021.
[72] Reynolds, C. W. (1987)Flocks, herds and schools
adistributedbehavioralmodel. Computer Craphics, vol. 21, n 4, pp. 25-34.
[73] Sabatier J., Cois O. et Oustaloup A. (2002) Commande de
systtmesnon entiers par placement de pôles. Conférence
Internationale Francophone dd'Automatique. Nantes, France.
[74] Sun H.H. et Onaral B. (1983) A unified approach to
represent metal electrodepolarization. IEEE Transactions on Biomedical
Engineering , vo. 30, n7, pp. 399-406.
[75] Samko S.G., Kilbas A.A. et Marichev OI. (1993) Fractional
Integrals andDerivatives. Gordon and Breach Science Publishers
[76] Vinagre B.M., Podlubny I., Hernandez A. et FeliuV (2000)
Some approximations of fractional order operators used in control theoryand
applications, Fractional Calculus & applied Analysis, vol. 3 n 3, pp.
231-248.
[77] Vinagre B.M., Monje C.A., et Calder'on A.J. (2002).
Fractional order systems and fractional order actions. Tutorial workshop # 2 :
Fractional calculus applicationsn automatic control and robotics, 41st IEEE
CDC, Las vegas, USA.
[78] Vinagre B. M., Monje C. A., Calderon A. JChen YQ. et FeliuV
(2004). The frac tional integrator as a reference function.In : Proceedings of
the lst IFAC Workshop on Fractional Di~erentiation and itsApplications,
Bordeaux France.
[79] Xue D.Y. et Chen Y.Q. (2005) Sub-Optimum Rational
Approximation to Fractional Order Linear SystemsProceedings of the ASME 2005
International Design Engii neering Technical Conferences Computers and
Informationn Engineering Confee rence. long Beach, California, USA.
[80] Xue D., Zhao C. et Chen Y.Q. (2006) A
ModiifiedApproximationMethod ofFractional Order System. Proceedings ofthe
IEEEInternational Conferenceon Mechatronics and Automation. Luoyang, china.
Conférence sur le Génie Electrique . CGE'07, 16-17
Avril 2007AlgerAlgérie