References

  1. [AGA 53] AGARWAL R.P., “A propos d’une note de M. Pierre Humbert”, Comptes Rendus de l’Académie des Sciences, Paris, vol. 236, no. 21, pp. 2031–2032, 1953.
  2. [AGR 04] AGRAWAL O.P., “A general formulation and solution scheme for fractional optimal control problems”, Nonlinear Dynamics, vol. 38, pp. 323–337, 2004.
  3. [AGR 07] AGRAWAL O.P., KUMAR P., “Comparison of five numerical schemes for fractional differential equations”, in SABATIER J. et al. (eds), Advances in Fractional Calculus, pp. 43–60, Springer, New York, USA, 2007.
  4. [AGU 14] AGUILA-CAMACHO N., DUARTE-MERMOUD M.A., GALLEGOS J.A., “Lyapunov functions for fractional order systems”, Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2951–2957, 2014.
  5. [ALG 95] ALGER P.L., Induction Machines. Their Behavior and Uses, Taylor & Francis, Milton Park, UK, 1995.
  6. [ANG 65] ANGOT A., Compléments de mathématiques, Editions de la Revue d’Optique, 1965.
  7. [AUV 80] AUVRAY J., Electronique des signaux analogiques, Collection Dunod Université, Bordas, Paris, France, 1980.
  8. [BAG 85] BAGLEY R.L., TORVIK P.J., “Fractional calculus in the transient analysis of viscoelastically damped structures”, AIAA Journal, vol. 23, no. 6, pp. 918–925, 1985.
  9. [BAL 13] BALACHANDRAN K., GOVINDARAJ K., ORTIGUEIRA M.D. et al., “Observability and controllability of fractional linear dynamical systems”, IFAC Workshop FDA’13, vol. 6 Part 1, Grenoble, France, pp. 893–898, 2013.
  10. [BAL 06] BALEANU D., “Fractional Hamiltonian analysis of irregular systems”, Signal Processing, vol. 26, pp. 2632–2636, 2006.
  11. [BAR 04] BARBOSA R.S., MACHADO J.A.R., FERREIRA I.M., “Tuning of PID controllers based on Bode’s ideal transfer function”, Non Linear Dynamics, vol. 38, pp. 305–321, 2004.
  12. [BAR 07] BARBOSA R.S., TENREIRO MACHADO J.A., VINAGRE B.M. et al., “Analysis of the Van der Pol oscillator containing derivatives of fractional order”, Journal of Vibration and Control, vol. 13, nos 9–10, pp. 1291–1301, 2007.
  13. [BAT 01] BATTAGLIA J.L., COIS O., PUISEGUR L. et al., “Solving an inverse heat conduction problem using a non-integer identified model”, International Journal of Heat and Mass Transfer, vol. 44, no. 14, pp. 2671–2680, 2001.
  14. [BAT 02] BATTAGLIA J.L., Méthodes d’identification de modèles à dérivées d’ordre non entier et de réduction modale. Application à la résolution de problèmes thermiques inverses dans les systèmes industriels, Habilitation à Diriger des Recherches, Université Bordeaux 1, 2002.
  15. [BEN 04] BENCHELLAL A., BACHIR S., POINOT T. et al., “Identification of a non-integer model of induction machines”, IFAC Workshop FDA’2004, Bordeaux, France, pp. 400–407, 2004.
  16. [BEN 06] BENCHELLAL A., POINOT T., TRIGEASSOU J.C., “Approximation and identification of diffusive interface by fractional models”, Signal Processing, vol. 86, no. 10, pp. 2712–2727, 2006.
  17. [BEN 08a] BENCHELLAL A., Modélisation des interfaces de diffusion à l’aide d’opérateurs d’intégration fractionnaires, PhD Thesis, University of Poitiers, France, 2008.
  18. [BEN 08b] BENCHELLAL A., POINOT T., TRIGEASSOU J.C., “Fractional modeling and identification of a thermal process”, Journal of Vibration and Control, vol. 14, nos 9–10, pp. 1403–1414, 2008.
  19. [BEN 93] BENNET S., “A history of control engineering”, vol. 1: 1800–1930 and vol. 2: 1930–1955, IEE Control Engineering Series, Peter Peregrinus, 1979 and 1993.
  20. [BET 06] BETTAYEB M., DJENNOUNE S., “A note on the controllability and the observability of fractional dynamic systems”, IFAC FDA’06 Workshop, Porto, Portugal, 2006.
  21. [BET 08] BETTAYEB M., DJENNOUNE S., “New results on the controllability and observability of fractional dynamical systems”, Journal of Vibration and Control, vol. 14, pp. 1531–1541, 2008.
  22. [BOD 45] BODE H.W., Network Analysis and Feedback Amplifier Design, Van Nostrand, New York, USA, 1945.
  23. [BON 00] BONNET C., PARTINGTON J.-R., “Coprime factorization and stability of fractional differential systems”, Systems and Control Letters, vol. 41, pp. 167–174, 2000.
  24. [BOS 86] BOSE B.K., Power Electronics and AC Drives, Prentice-Hall, New Jersey, USA, 1986.
  25. [BOU 67] BOUDAREL R., DELMAS J., GUICHET P., Commande optimale des processus, vols 1–4, Dunod, Paris, France, 1967.
  26. [BOY 94] BOYD S., EL GHAOUI L., FERON E. et al., Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, USA, 1994.
  27. [CAN 05a] CANAT S., FAUCHER J., “Modeling, identification and simulation of induction machine with fractional derivative”, in LE MEHAUTE A. et al. (eds), Fractional Differentiation and its Applications, Ubooks Verlag, Augsburg, Germany, 2005.
  28. [CAN 05b] CANAT S., Contribution à la modélisation dynamique d’ordre non entier de la machine asynchrone à cage, Thesis, INPT, France, 2005.
  29. [CAP 69] CAPUTO M., Elasticita e Dissipazione, Zanichelli, Bologna, Italy, 1969.
  30. [CHA 82] CHATELAIN J.D., DESSOULAVY R., Electronique, vols 1 and 2, Dunod, Paris, France, 1982.
  31. [CHA 05] CHATTERJEE A., “Statistical origins of fractional derivatives in viscoelasticity”, Journal of Sound and Vibration, vol. 284, pp. 1239–1245, 2005.
  32. [CHE 84] CHEN C.T., Linear System Theory and Design, Oxford University Press, UK, 1984.
  33. [CHE 14] CHEN D., ZHANG R., LIN X. et al., “Fractional order Lyapunov stability theorem and its application in synchronization of complex dynamical networks”, Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 12, pp. 4105–4121, 2014.
  34. [COI 01] COIS O., OUSTALOUP A., POINOT T. et al., “Fractional state variable filter for system identification by fractional model”, European Control Conference ECC’2001, Porto Portugal, 3–5 September, 2001.
  35. [COI 02] COIS O., Systèmes linéaires non entier et identification par modèle non entier: application en thermique, PhD Thesis, University of Bordeaux, France, 2002.
  36. [COL 33] COLE K.S., “Electric conductance of biological systems”, Proceedings Cold Spring Harbor Symposia on Quantitative Biology, pp. 107–116, 1933.
  37. [COU 85] COULOMB J.L., SABONNADIERE J.C., CAO en électrotechnique, Hermès, Paris, France, 1985.
  38. [CUR 95] CURTAIN R.F., ZWART H.J., An Introduction to Infinite Dimensional Linear Systems Theory, Springer-Verlag, Berlin, Germany, 1995.
  39. [DAD 11] DADRAS S., MOMENI H.R., “A new fractional observer design for fractional order nonlinear systems”, Proceedings of the ASME Conference IDETC 2011, Washington, USA, 28–31 August 2011.
  40. [DAS 11] DAS S., Functional Fractional Calculus, Springer-Verlag, Berlin, Germany, 2011.
  41. [DAS 13] DAS S., CHATTERJEE A., “Numerical stability analysis of linear incommensurate fractional order systems”, Journal of Computational and Nonlinear Dynamics, vol. 6, no. 4, 6 pages, May 2013.
  42. [DEN 69] DENIS-PAPIN M., KAUFMANN A., Cours de calcul matriciel appliqué, Albin Michel, Paris, France, 1969.
  43. [DIE 02] DIETHELM K., FORD N.J., “Numerical solution of the Bagley-Torvik equation”, BIT, vol. 42, no. 3, pp. 490–507, 2002.
  44. [DIE 08] DIETHELM K., “An investigation of some non-classical methods for the numerical approximation of Caputo-type fractional derivatives”, Numerical Algorithms, vol. 47, pp. 361–390, 2008.
  45. [DIE 10] DIETHELM K., “Appendix C: Numerical solution of fractional equations”, in DIETHELM K. et al. (eds), The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, pp. 195–225, 2010.
  46. [DJA 08] DJAMAH T., DJENNOUNE S., BETTAYEB M., “Fractional order system identification”, JTEA 2008, Hammamet, Tunisia, 2008.
  47. [DJE 12] DJENNOUNE S., KATZANSTSIS N., SABATIER J., “Discussion on observability and pseudo-state estimation of fractional order systems”, European Journal of Control, vol. 18, pp. 272–276, 2012.
  48. [DJE 13] DJENNOUNE S., BETTAYEB M., “Optimal synergetic control for fractional order systems”, Automatica, vol. 49, pp. 2243–2249, 2013.
  49. [DOR 67] DORF R.C., Les variables d’état dans l’analyse et la synthèse des systems automatiques, translated from English by NASLIN P., Dunod, Paris, France, 1967.
  50. [DU 11] DU M., WANG Z., “Initialized fractional differential equations with Riemann-Liouville fractional order derivative”, ENOC 2011 Conference, Rome, Italy, July 2011.
  51. [DU 16] DU B., WEI Y., LIANG S. et al., “Estimation of exact initial states of fractional order systems”, Nonlinear Dynamics, vol. 86, pp. 2061–2070, 2016.
  52. [DUG 97] DUGARD L., VERRIEST E.-I., Stability and Control of Time Delay Systems, Lectures Notes in Control and Information Sciences, vol. 228, Springer-Verlag, Berlin, Germany, 1997.
  53. [DZI 06] DZIELINSKI A., SIEROCIUK D., “Observer for discrete fractional order state-space systems”, FDA’06 Workshop, vol. 2, pp. 511–516, 2006.
  54. [EYK 74] EYKHOFF P., System Identification, John Wiley and Sons, New York, USA, 1974.
  55. [FAH 11] FAHD J. et al., “On the Mittag-Leffler stability of Q-fractional nonlinear dynamical systems”, Proceedings of the Romanian Academy, Series A, vol. 12, no. 4/2011, pp. 309–314, 2011.
  56. [FAH 12] FAHD J. et al., “On the stability of some discrete fractional non-autonomous systems”, Abstract an Applied Analysis, vol. 2012, Article ID 476581, 9 p., 2012. doi:10.1155/2012/476581.
  57. [FAR 82] FARLOW S.J., Partial Differential Equations for Scientists and Engineers, John Wiley and Sons, New York, USA, 1982.
  58. [FRA 68] FRANKLIN J.N., Matrix Theory, Prentice-Hall, New Jersey, USA, 1968.
  59. [FRI 86] FRIEDLAND B., Control System Design: An Introduction to State-space Methods, McGraw-Hill, New York, USA, 1986.
  60. [FUK 03] FUKUNAGA M., SHIMIZU N., “Initial condition problems of fractional viscoelastic equations”, Proceedings of the ASME Conference DETC’03, Chicago, USA, 2003.
  61. [FUK 04] FUKUNAGA M., SHIMIZU N., “Role of pre-histories in the initial value problems of fractional viscoelastic equations”, Nonlinear Dynamics, vol. 38, pp. 207–220, 2004.
  62. [GAB 11a] GABANO J.D., POINOT T., “Fractional modeling and identification of thermal systems”, Signal Processing, vol. 11, no. 3, pp. 531–541, 2011.
  63. [GAB 11b] GABANO J.D., POINOT T., “Estimation of thermal parameters using fractional modeling”, Signal Processing, vol. 11, no. 4, pp. 938–948, 2011.
  64. [GAM 11] GAMBONE T., HARTLEY T.T., ADAMS J. et al., “An experimental validation of the initialization response in fractional order systems”, Proceedings of IDETC/CIE FDTA’2011 Conference, August, Washington, DC, 2011.
  65. [GAN 66] GANTMACHER F.R., Théorie des matrices, Volumes 1 and 2, Dunod, Paris, France, 1966.
  66. [GEL 00] GELFAND I.M., FOMIN S.V., Calculus of Variations, translated from Russian, Dover Publications, New York, USA, 2000.
  67. [GIB 63] GIBSON J., Nonlinear Automatic Control, McGraw-Hill, New York, USA, 1963.
  68. [GIL 63] GILBERT E.G., “Controllability and observability in multivariable control system”, SIAM Journal on Control, Series A, vol. 2, no. 1, pp. 128–151, 1963.
  69. [GIL 90] GILLE J.C., DECAULNE P., PELEGRIN M., Théorie et calcul des asservissements linéaires, Dunod-Bordas, Paris, France, 1990.
  70. [GOR 02] GORENFLO R., LOUTCHKO J., LUCHKO Y., “Computation of the Mittag-Leffler function Eα,β (z) and its derivative”, Journal of Fractional Calculus and Applied Analysis, vol. 5, no. 4, 2002.
  71. [HAN 96] HANUS R., BOGAERTS P., Introduction à l’automatique. Vol. 1: Systèmes continus, De Boeck & Larcier, Brussels, Belgium, 1996.
  72. [HAR 98] HARRIS J.W., STOCKER H., Handbook of Mathematics and Computational Science, Springer-Verlag, Berlin, Germany, 1998.
  73. [HAR 95] HARTLEY T.T., LORENZO C.F., QAMMER H.K., “Chaos in fractional order Chuaʼs system”, IEEE Transactions on Circuits and Systems I. Fundamental Theory and Applications, vol. 42, no. 8, pp. 485–490, 1995.
  74. [HAR 02] HARTLEY T.T., LORENZO C.L., “Dynamics and control of initialized fractional order system”, Nonlinear Dynamics, vol. 29, pp. 201–233, 2002.
  75. [HAR 07] HARTLEY T.T., LORENZO C.F., “Application of incomplete gamma functions to the initialization of fractional order systems”, Proceedings of the ASME Conference DETC 2007, Las Vegas, 4–7 September 2007.
  76. [HAR 09a] HARTLEY T.T., LORENZO C.F., “The error incurred in using the Caputo derivative Laplace transform”, Proceedings of the ASME IDET-CIE Conferences, San Diego, USA, 2009.
  77. [HAR 09b] HARTLEY T.T., LORENZO, C.F., “The initialization response of linear fractional order system with constant History function”, 2009 ASME /IDETC, San Diego, USA, 2009.
  78. [HAR 09c] HARTLEY T.T., LORENZO C.F., “The initialization response of linear fractional order systems with ramp history functions”, Proceedings of the ASME Conference IDETC 2009, San Diego, USA, 30 August–2 September 2009.
  79. [HAR 11] HARTLEY T.T., LORENZO C.F., “The initialization response of multi term linear fractional order systems with constant history functions”, Proceedings of IDETC/CIE FDTA’2011 Conference, Washington DC, USA, August 2011.
  80. [HAR 13] HARTLEY T.T., LORENZO C.F., TRIGEASSOU J.C. et al., “Equivalence of history function based and infinite dimensional state initializations for fractional order operators”, ASME Journal of Computational and Nonlinear Dynamics, vol. 8, no. 4, 2013.
  81. [HAR 15a] HARTLEY T.T., TRIGEASSOU J.C., LORENZO C.F. et al., “Energy storage and loss in fractional order systems”, ASME Journal of Computational and Nonlinear Dynamics CND 14-1113, vol. 10, no. 6, 2015.
  82. [HAR 15b] HARTLEY T.T., LORENZO C.F., “Realizations for determining the energy stored in fractional order operators”, ASME IDETC-CIE Conference, Boston, USA, August 2015.
  83. [HAR 15c] HARTLEY T.T., TRIGEASSOU J.C., LORENZO C.F. et al., “Initialization energy in fractional order systems”, Proceedings of the ASME Conference IDETC/CIE 2015, Boston, USA, 2015.
  84. [HEL 00] HELECHEWITZ D., Analyse et simulation de systèmes différentiels fractionnaires et pseudo-différentiels sous representation diffusive, PhD Thesis, ENST Paris, 18 December 2000.
  85. [HEL 98] HELESCHEWITZ D., MATIGNON D., “Diffusive realizations of fractional integro-differential operators: structural analysis under approximation”, Conference IFAC, System, Structure and Control, vol. 2, pp. 243–248, Nantes, France, July 1998.
  86. [HIM 72] HIMMELBLAU D.M., Applied Nonlinear Programming, McGraw-Hill, New York, USA, 1972.
  87. [HOL 89] HOLMAN J.P., Heat Transfer, McGraw-Hill, New York, USA, 1989.
  88. [HOT 98] HOTZEL R., Contributions à la théorie structurelle et à la commande des systèmes linéaires fractionnaires, PhD Thesis, University of Paris XI, Orsay, 1998.
  89. [HUL 15] HU J.B., LU G.P., ZHANG S.H., “Lyapunov stability theorem about fractional system without and with delay”, Communications in Nonlinear Science and Numerical Simulation, vol. 20, no. 3, pp. 905–913, 2015.
  90. [HUR 95] HURWITZ A., “Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln niet negativen reelen Theilenbesitzt”, Mathematische Annalen, vol. 46, pp. 273–284, 1895.
  91. [HUS 09] HUSSON R. (ed.), Control Methods for Electrical Machines, ISTE Ltd, London and John Wiley and Sons, New York, USA, 2009.
  92. [HWA 06] HWANG C., CHENG Y.-C., “A numerical algorithm for stability testing of fractional delay systems”, Automatica, vol. 42, pp. 825–831, 2006.
  93. [IRW 99] IRWIN J.D., WU C.H., Basic Engineering Circuit Analysis, Prentice Hall, New Jersey, USA, 1999.
  94. [JAL 10] JALLOUL A., JELASSI K., TRIGEASSOU J.C., “Fractional modeling of rotor skin effect in induction machines”, IFAC Workshop FDA ‘10, Badajoz, Spain, 2010.
  95. [JAL 12] JALLOUL A., Modélisation et identification des effets de fréquence dans la machine asynchrone par approche d’ordre non entire, PhD Thesis, University of Tunis, Tunisia, 2012.
  96. [JAL 13] JALLOUL A., TRIGEASSOU J.C., JELASSI K. et al., “Fractional modeling of rotor skin effect in induction machines”, Nonlinear Dynamics, vol. 73, nos 1–2, pp. 801–813, 2013.
  97. [JOO 86] JOOS G., Theoretical Physics, Dover Publications, New York, USA, 1986.
  98. [KAB 97] KABBAJ H., Identification d’un modèle circuit prenant en compte les effets de fréquence dans une machine asynchrone à cage d’écureuil, Thesis, INPT France, 1997.
  99. [KAI 80] KAILATH T., Linear Systems, Prentice Hall Inc, New Jersey, USA, 1980.
  100. [KAL 60] KALMAN R.E., “On the general theory of control system”, Proceedings of the First IFAC Congress Automatic Control, vol. 1, pp. 481–492, Moscow, Russia, 1960.
  101. [KHA 15a] KHADHRAOUI A., JELASSI K., TRIGEASSOU J.C. et al., “Identification of fractional model by least squares method and instrumental variable”, Journal of Computational and Nonlinear Dynamics, vol. 10, no. 5, 2015.
  102. [KHA 15b] KHADHRAOUI A., JELASSI K., TRIGEASSOU J.C. et al., “Initialization of identification of fractional model by output-error technique”, Journal of Computational and Nonlinear Dynamics, vol. 11, no. 2, 2015.
  103. [KHA 16] KHADHRAOUI A., Contribution à l’identification des systèmes d’ordre non entier: application à l’identification des effets de peau dans les barres rotoriques d’une machine asynchrone, PhD Thesis, University of Tunis, Tunisia, 2016.
  104. [KHA 96] KHALIL H.K., Nonlinear Systems, Prentice Hall, New Jersey, USA, 1996.
  105. [KHA 01] KHAORAPAPONG T., Modélisation d’ordre non entier des effets de fréquence dans les barres rotoriques d’une machine asyncrone, Thesis, France, 2001.
  106. [KIR 04] KIRK D.E., Optimal Control Theory. An Introduction, Dover Publications, New York, USA, 2004.
  107. [KOR 68] KORN G.A., KORN T.M., Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York, USA, 1968.
  108. [KRA 92] KRANIANSKAS P., Transforms in Signals and Systems, Addison Wesley, Boston, USA, 1992.
  109. [KRA 63] KRASOVSKII N.N., Stability of Motion, Stanford University Press, Palo Alto, USA, 1963.
  110. [KUN 86] KUNDERT K.S., SANGIOVANNI-VINCENTELLI A., “Simulation of nonlinear circuits in the frequency domain”, IEEE Transactions on Computer Aided Design of Integrated Circuits, vol. CAD-5, no. 4, October 1986.
  111. [KUP 17] KUPPER M., GIL I.S., HOHMANN S., “Distributed and decentralized Kalman filtering for cascaded fractional order systems”, American Control Conference ACC 2017, Seattle, USA, May 2017.
  112. [LAN 89] LANDAU I.D., Identification et commande de systèmes, Hermès, Paris, France, 1989.
  113. [LAS 61] LA SALLE J., LEFSCHETZ S., Stability by Liapunovʼs Direct Method with Applications, Academic Press, Cambridge, USA, 1961.
  114. [LEM 83] LE MÉHAUTÉ A., CREPY G., “Introduction to transfer and motion in fractal media: the geometry of kinetics”, Solid State Ionics, vols 9–10, pp. 17–30, 1983.
  115. [LEP 80] LEPAGE W.R., Complex Variables and the Laplace Transform for Engineers, Dover Publications, New York, USA, 1980.
  116. [LES 11] LESZCZYNSKI J.S., An Introduction to Fractional Mechanics, Częstochowa University of Technology, Poland, 2011.
  117. [LEV 59] LEVY E.C., “Complex curve fitting”, IRE Transactions on Automatic Control, vol. AC-4, pp. 37–43, 1959.
  118. [LEV 64] LEVINE L., Methods for Solving Engineering Problems Using Analog Computers, McGraw-Hill, New York, USA, 1964.
  119. [LI 09] LI Y., CHEN Y.Q., PODLUBNY I., “Mittag Leffler stability of fractional order nonlinear dynamic systems”, Automatica, vol. 45, pp. 1965–1969, 2009.
  120. [LI 10] LI Y., CHEN Y.Q., PODLUBNY I., “Stability of fractional order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability”, Computers and Mathematics with Applications, vol. 59, pp. 1810–1821, 2010.
  121. [LI 14] LI Y., CHEN Y.Q., “Lyapunov stability of fractional order nonlinear systems: a distributed order approach”, ICFDA’14, 23–25 June 2014.
  122. [LIN 00] LIN J., POINOT T., TRIGEASSOU J.C., “Parameter estimation of fractional systems: application to the modeling of a lead-acid battery”, 12th IFAC Symposium on System Identification, SYSID 2000, USA, 2000.
  123. [LIN 01a] LIN J., Modélisation et identification des systèmes d’ordre non entier, PhD Thesis, University of Poitiers, France, 2001.
  124. [LIN 01b] LIN J., POINOT T., TRIGEASSOU J.C., “Parameter estimation of fractional systems. Application to heat transfer”, European Control Conference ECC 2001, Porto, Portugal, pp. 2644–2649, 2001.
  125. [LIO 71] LIONS J.L., Optimal Control of Systems Governed by Partial Differential Equations, Springer, New York, USA, 1971.
  126. [LJU 87] LJUNG L., System Identification: Theory for the User, Englewood Cliffs, New Jersey, USA, 1987.
  127. [LOR 01] LORENZO C.F., HARTLEY T.T., “Initialization in fractional order systems”, Proceedings of the European Control Conference (ECC’01), Porto, Portugal, pp. 1471–1476, 2001.
  128. [LOR 08a] LORENZO, C.F., HARTLEY, T.T., “Initialization of fractional differential equation”, ASME Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, 2008.
  129. [LOR 08b] LORENZO C.F., HEARTLEY T.T., “Initialization of fractional order operators and fractional differential equations”, Special issue on Fractional Calculus of ASME Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, 021101, April 2008.
  130. [LOR 11] LORENZO C., HARTLEY T., “Time-varying initialization and Laplace transform of the Caputo derivative: with order between zero and one”, Proceedings of IDETC/CIE FDTA’2011 Conference, Washington DC, USA, August 2011.
  131. [LUE 66] LUENBERGER D.G., “Observers for multivariable systems”, IEEE Transactions on Automatic Control, vol. AC-11, no. 2, pp. 190–197, 1966.
  132. [LYA 07] LYAPUNOV A., “Problème général de la stabilité du mouvement”, Annales de la Faculté des Sciences de Toulouse, vol. 9, 1907.
  133. [MAA 91] MAAMRI N., TRIGEASSOU J.C., OUSTALOUP A., “Time moments and CRONE control”, IMACS Congress, Lille, France, 1991.
  134. [MAA 09] MAAMRI N., TRIGEASSOU J.C., MEHDI D., “A frequency approach to analyze the stability of delayed fractional differential equations”, Proceedings of the European Control Conference ECC’09, Budapest, Hungary, August 2009.
  135. [MAA 10] MAAMRI N., TRIGEASSOU J.C., TENOUTIT M., “On fractional PI and PID controllers”, Proceedings of IFAC Workshop FDA’10, Badajoz, Spain.
  136. [MAA 14] MAAMRI N., TARI M., TRIGEASSOU J.C., “Physical interpretation and initialization of the fractional integrator”, ICFDA’14 23–25 June 2014.
  137. [MAA 15] MAAMRI N., TARI M., TRIGEASSOU J.C., “On the fractional modeling of the diffusive interface”, Proceedings of the ASME Conference IDETC/CIE 2015, Boston, USA, 2015.
  138. [MAA 16] MAAMRI N., TRIGEASSOU J.C., “Lyapunov stability of nonlinear fractional systems: the Van der Pol oscillator”, ICFDA’16 Serbia 2016.
  139. [MAA 17] MAAMRI N., TARI M., TRIGEASSOU J.C., “Improved initialization of fractional order systems”, 20th World IFAC Congress, Toulouse, France, pp. 8567–8573, 2017.
  140. [MAG 06] MAGIN R.L., Fractional Calculus in Bioengineering, Begell House, Danbury, USA, 2006.
  141. [MAL 08] MALTI R., VICTOR S., OUSTALOUP A., “Advances in system identification using fractional models”, Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, 7 pages, 2008.
  142. [MAN 60] MANABE S., “The noninteger integral and its application to control systems”, Journal of the Institute of Electrical Engineers of Japan, pp. 589–597, May 1960.
  143. [MAO 15] MAOLIN D., ZAIHUA W., “Correcting the initialization of models with fractional derivatives via history dependent conditions”, Acta Mechanica Sinica, August 2015. doi: 10.1007/s10409-015-0469-7.
  144. [MAR 63] MARQUARDT D.W., “An algorithm for least squares estimation of nonlinear parameters”, Journal of the Society for Industrial and Applied Mathematics, vol. 11, no. 2, pp. 431–441, 1963.
  145. [MAR 93] MARCUS M., Matrices and MATLABTM: A Tutorial, Prentice Hall, New Jersey, USA, 1993.
  146. [MAT 94] MATIGNON D., Représentations en variables d’état de modèles de guides d’ondes avec dérivation fractionnaire, PhD Thesis, University of Paris XI, Orsay, France, 1994.
  147. [MAT 96] MATIGNON D., D’ANDRÉA-NOVEL B., “Some results on controllability and observability of finite dimensional fractional differential systems”, Computational Engineering in Systems Applications Lille France, vol. 2, pp. 952–956, 1996.
  148. [MAT 97] MATIGNON D., D’ANDRÉA-NOVEL B., “Observer based controllers for fractional differential systems”, Proceedings of the CDC’97, San Diego, USA, pp. 4967–4972, December 1997.
  149. [MAT 98] MATIGNON D., “Stability properties for generalized fractional differential systems”, Proceedings of the ESSAIM, vol. 5, pp. 145–158, 1998.
  150. [MAT 10] MATIGNON D., “Optimal control of fractional systems: a diffusive formulation”, Proceedings of the MTNS 2010, Budapest, Hungary, July 2010.
  151. [MEN 73] MENDEL J.M., Discrete Techniques of Parameter Estimation, Marcel Dekker, New York, USA, 1973.
  152. [MIL 93] MILLER K.S., ROSS B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, New York, USA, 1993.
  153. [MIT 03] MITTAG-LEFFLER G.M., “Sur la nouvelle fonction Eα (x)”, Comptes Rendus de l’Académie des Sciences, Paris, France, vol. 137, pp. 554–558, 1903.
  154. [MOK 97] MOKHTARI M., MESBAH A., Apprendre et maîtriser MATLABTM, Springer, New York, USA, 1997.
  155. [MOM 04] MOMANI S., HADID S., “Lyapunov stability solutions of fractional integro-differential equations”, International Journal of Mathematics and Mathematical Sciences, vol. 47, pp. 2503–2507, 2004.
  156. [MON 05a] MONJE C.A., VINAGRE B.M., CHEN Y.Q. et al., “Optimal tunings for fractional fractional PID controllers”, in LE MEHAUTE A. et al. (eds), Fractional Differentiation and Its Applications, pp. 675–686, 2005.
  157. [MON 05b] MONTSENY G., Représentation Diffusive, Hermès Lavoisier, Paris, France, 2005.
  158. [MON 98] MONTSENY G., “Diffusive representation of pseudo differential time operators”, Proceedings of ESSAIM, vol. 5, pp. 159–175, 1998.
  159. [MON 10] MONJE C.A., CHEN Y.Q., VINAGRE B.M. et al., Fractional Order Systems and Control, Springer-Verlag, Berlin, Germany, 2010.
  160. [MOR 10] MORRIS K., “Control of systems governed by partial differential equations”, The IEEE Control Theory Handbook, CRC Press, Florida, USA, 2010.
  161. [MUL 09] MULLHAUPT P., Introduction à l’analyse et à la commande des systèmes non linéaires, Presses Polytechniques et Universitaires Romandes, Lausanne, Switzerland, 2009.
  162. [NAS 68] NASLIN P., Théorie de la commande et variables d’état, Ecole Supérieure d’Electricité, 1968.
  163. [NDO 11] N’DOYE I., DAROUACH M., ZASADZINSKI M. et al., “Observer design for singular fractional-order systems”, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, USA, 2011.
  164. [NIC 97] NICULESCU S.I., Systèmes à retard, Diderot Editeur Arts et Sciences, Paris, France, 1997.
  165. [NOR 86] NORTON J.P., An Introduction to Identification, Academic Press, Cambridge, USA, 1986.
  166. [NOU 91] NOUGIER J.P., Méthodes de calcul numérique, Masson, Paris, France, 1991.
  167. [NYQ 32] NYQUIST H., “Regeneration theory”, Bell System Technical Journal, vol. 11, pp. 126–147, 1932.
  168. [OLD 70] OLDHAM K.B., SPANIER J., “The replacement of Fick’s law by a formulation involving semi-differentiation”, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, vol. 26, pp. 331–341, 1970.
  169. [OLD 72] OLDHAM K.B., “A signal independent electro-analytical method”, Analytical Chemistry, vol. 44, no. 1, pp. 196–198, 1972.
  170. [OLD 74] OLDHAM K.B., SPANIER J., The Fractional Calculus, Academic Press, Cambridge, USA, 1974.
  171. [ORT 98] ORTEGA R., LORIA A., NICKLASSON P.J. et al., Passivity Based Control of Euler Lagrange Systems, Springer-Verlag, Berlin, Germany, 1998.
  172. [ORT 03] ORTIGUEIRA M.D., “On the initial conditions in continuous-time fractional linear systems”, Signal Processing, vol. 83, pp. 2301–2309, 2003.
  173. [ORT 08] ORTIGUEIRA M.D., COITO F.J., “Initial conditions: what are we talking about?”, 3rd IFAC Workshop, FDA’08, Ankara, Turkey, 5–7 November 2008.
  174. [ORT 11] ORTIGUEIRA M.D., Fractional Calculus for Scientists and Engineers, Springer Science, New York, USA, 2011.
  175. [ORT 15] ORTIGUEIRA M.D., TENREIRO M.J., RIVERO M. et al., “Integer/fractional decomposition of the impulse response of fractional linear systems”, Signal Processing, vol. 114, pp. 85–88, 2015.
  176. [ORT 18] ORTIGUEIRA M.D., LOPES A.M., TENREIRO M.J., “On the computation of the multi-dimensional Mittag-Leffler function”, Communications in Nonlinear Science and Numerical Simulation, vol. 53, pp. 278–287, 2018.
  177. [OUS 81] OUSTALOUP A., “Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation”, IEEE Transactions on Circuits and Systems, vol. 28, no. 10, pp. 1007–1009, 1981.
  178. [OUS 83] OUSTALOUP A., Systèmes asservis linéaires d’ordre fractionnaire, Masson, Paris, France, 1983.
  179. [OUS 91] OUSTALOUP A., La commande CRONE, Hermès, Paris, France, 1991.
  180. [OUS 95a] OUSTALOUP A., La dérivation non entière: théorie, synthèse et applications, Hermès, Paris, France, 1995.
  181. [OUS 95b] OUSTALOUP A., MATHIEU B., La commande CRONE, du scalaire au multivariable, Hermès, Paris, France, 1995.
  182. [OUS 00] OUSTALOUP A., LEVRON F., MATHIEU B. et al., “Frequency-band complex noninteger differentiator: characterization and synthesis”, Transactions on Circuits and Systems I; Fundamental Theory and Applications, vol. 47, no. 1, pp. 25–39, 2000.
  183. [OUS 05] OUSTALOUP A., COIS O., LE LAY L., Représentation et identification par modèle non entier, Hermès Lavoisier, Paris, France, 2005.
  184. [OUS 15] OUSTALOUP A., Diversity and Non-integer Differentiation for System Dynamics, ISTE Ltd, London, UK and John Wiley & Sons, New York, USA, 2015.
  185. [OWE 86] OWENS L., “Vannevar Bush and the differential analyzer: the text and context of an early computer”, Technology and Culture, vol. 27, no. 1, pp. 63–95, January 1986.
  186. [PAR 29] PARK R.H., “Two reaction theory of synchrone machines”, Transaction on AIEE, pp. 27–31, 1929.
  187. [PET 11] PETRAS I., Fractional Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer Verlag, Berlin, Germany, 2011.
  188. [POD 97] PODLUBNY I., DORCAK L., KOSTIAL I., “On fractional derivatives, fractional order systems and PID control”, Proceedings of the Conference on Decision and Control, San Diego, USA, 1997.
  189. [POD 99] PODLUBNY I., Fractional Differential Equations, Academic Press, Cambridge, USA, 1999.
  190. [POD 00] PODLUBNY I., “Matrix approach to discrete fractional calculus”, Journal of Fractional Calculus and Applied Analysis, vol. 3, no. 4, pp. 359–386, 2000.
  191. [POD 02a] PODLUBNY I., “Geometric and physical interpretation of fractional integration and fractional differentiation”, Fractional Calculus and Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002.
  192. [POD 02b] PODLUBNY I., PETRAS I., VINAGRE B.M. et al., “Analogue realizations of fractional order controllers”, Nonlinear Dynamics, vol. 29, nos 1–4, pp. 281–296, 2002.
  193. [POI 82] POINCARE H., “Mémoire sur les courbes limites définies par une équation différentielle”, Journal de Mathématiques, vol. 3, no. 8, pp. 251–296, 1882.
  194. [POI 02] POINOT T., TRIGEASSOU J.C., “Parameter estimation of fractional models: application to the modelling of diffusive systems”, 15th IFAC World Congress, Barcelona, Spain, 2002.
  195. [POI 03] POINOT T., TRIGEASSOU J.C., “A method for modeling and simulation of fractional systems”, Signal Processing, vol. 83, pp. 2319–2333, 2003.
  196. [POI 04] POINOT T., TRIGEASSOU J.C., “Identification of fractional systems using an output-error technique”, Nonlinear Dynamics, vol. 38, nos 1–4, pp. 133–154, 2004.
  197. [POL 87] POLOUJADOFF M., “The theory of three phase induction squirrel cage rotors”, Electrical Machines and Power Supplies, vol. 13, pp. 245–264, 1987.
  198. [RAG 47] RAGAZZINI J.R., RANDALL R.H., RUSSELL F.A., “Analysis of problems in dynamics by electronic circuits”, Proceedings of the IRE, vol. 35, no. 5, pp. 444–452, May 1947.
  199. [RAM 10] RAMDANI K., TUCSNAK M., WEISS G., “Recovering the initial state of an infinite dimensional system using observers”, Automatica, vol. 46, pp. 1616–162, 2010.
  200. [RAP 15] RAPAIC M.R., MALTI R., “On stability regions of fractional systems in the space of perturbed orders”, IET Research Journals, 9 pages, 2015.
  201. [RAP 16] RAPAIC M.R., MALTI R., “Stability of fractional incommensurate systems”, ICFDA Conference, Novi Sad, Serbia, pp. 424–431, 2016.
  202. [RAY 97] RAYNAUD H.F., ZERGAINOH A., “State-space representation of fractional linear filters”, Proceedings of the European Control Conference ECC 97, Brussels, Belgium, 1997.
  203. [RET 99] RETIERE N., IVANES M., “An introduction to electrical machine modeling by systems of non-integer order. Application to double-cage induction machines”, IEEE Transactions on Energy Conversion, vol. 14, no. 4, pp. 1026–1032, December 1999.
  204. [RIC 71] RICHALET J., RAULT A., POULIQUEN R., Identification des processus par la méthode du modèle, Gordon and Breach, London, UK, 1971.
  205. [RIC 91] RICHALET J., Pratique de l’identification, Hermès, Paris, France, 1991.
  206. [RIC 03] RICHARD J.P., “Time-delay Systems: an overview of some recent advances and open problems”, Automatica, vol. 39, pp. 1667–1694, 2003.
  207. [ROU 77] ROUTH E.J., A Treatise on the Stability of a Given State of Motion, MacMillan, London, UK, 1877.
  208. [SAB 06] SABATIER J., AOUN M., OUSTALOUP A. et al., “Fractional system identification for lead-acid battery state of charge estimation”, Signal Processing, vol. 86, pp. 2645–2657, 2006.
  209. [SAB 08a] SABATIER J. et al., “On stability and performances of fractional order systems”, 3rd IFAC Symposium FDA’08, Ankara, Turkey, 5–7 November 2008.
  210. [SAB 08b] SABATIER J. et al., “On a representation of fractional order systems: interests for the initial condition problem”, 3rd IFAC Workshop FDA’08, Ankara, Turkey, 5–7 November 2008.
  211. [SAB 09] SABATIER J., MERVEILLAUT M., FENETEAU L. et al., “On observability of fractional order systems”, Proceedings of the ASME IDET-CIE Conferences, San Diego, California, USA, 2009.
  212. [SAB 10a] SABATIER J., MERVEILLAUT M., MALTI R. et al., “How to impose physically coherent initial conditions to a fractional system”, Communications in Non Linear Science and Numerical Simulation, vol. 15, no. 5, pp. 1318–1326, 2010.
  213. [SAB 10b] SABATIER J., MOZE M., FARGES C., “LMI stability conditions for fractional order systems”, Computers and Mathematics with Applications, vol. 9, pp. 1594–1609, 2010.
  214. [SAB 12] SABATIER J., FARGES C., MERVEILLAUT M. et al., “On observability and pseudo state estimation of fractional order system”, European Journal of Control, vol. 18, no. 3, pp. 260–271, 2012.
  215. [SAB 13] SABATIER J., FARGES C., TRIGEASSOU J.C., “A stability test for non commensurate fractional order systems”, Systems and Control Letters, vol. 62, no. 9, pp. 739–746, 2013.
  216. [SAB 14] SABATIER J., FARGES C., TRIGEASSOU J.C., “Fractional systems state space description: some wrong ideas and proposed solutions”, Journal of Vibration and Control, vol. 20, no. 7, pp. 1076–1084, 2014.
  217. [SAB 16] SABATIER J., FARGES C., FADIGA L., “Approximation of a fractional order model by an integer order model: a new approach taking into account approximation error as an uncertainty”, Journal of Vibration and Control, vol. 22, no. 8, pp. 2069–2082, 2016.
  218. [SAD 10] SADATI S.J., BALEANU D., RANJBAR A. et al., “Mittag Leffler stability theorem for fractional nonlinear systems with delay”, Abstract and Applied Analysis, vol. 2010, ID 108651, 2010.
  219. [SAM 93] SAMKO S.G., KILBAS A.A., MARITCHEV O.I., “Fractional integrals and derivatives. Theory and applications”, Translated from Russian, Gordon and Breach, London, UK, 1993.
  220. [SAS 10] SASTRY S., Nonlinear Systems. Analysis, Stability and Control, Springer-Verlag, Berlin, Germany, 2010.
  221. [SCH 98] SCHWARTZ L., Méthodes mathématiques pour les sciences physiques, Ecole Polytechnique, Hermann, Paris, France, 1998.
  222. [SLO 91] SLOTINE J.J.E., LI W., Applied Nonlinear Control, Prentice Hall, New Jersey, USA, 1991.
  223. [SPI 65] SPIEGEL M.R., Laplace Transforms, McGraw-Hill, New York, USA, 1965.
  224. [STE 94] STENGEL R.F., Optimal Control and Estimation, Dover Publications, New York, USA, 1994.
  225. [STR 15] STROGATZ S.H., Nonlinear Dynamics and Chaos, Westview Press, Boulder, USA, 2015.
  226. [TAR 16a] TARI M., MAAMRI N., TRIGEASSOU J.C., “Initial conditions and initialization of fractional systems”, ASME Journal of Computational and Nonlinear Dynamics, vol. 11, no. 4, 2016.
  227. [TAR 16b] TARI M., MAAMRI N., TRIGEASSOU J.C., Observability and Observation of Commensurate Order Fractional Systems, ICFDA’16, Serbia, 2016.
  228. [TAR 16c] TARI M., Etat distribué, pseudo-état, observation et initialisation des systèmes fractionnaires, PhD Thesis, University of Poitiers, France, 2016.
  229. [TEN 12] TENOUTIT M., MAAMRI N., TRIGEASSOU J.C., “Tuning of a new class of robust fractional-order proportional-integral-derivative controllers”, Journal of Systems and Control Engineering, vol. 226, no. 4, pp. 486–496, 2012.
  230. [TEN 13] TENOUTIT M., Définition et réglage de correcteurs robustes d’ordre fractionnaire, PhD Thesis, University of Poitiers, France, 2013.
  231. [TEN 14] TENREIRO MACHADO J., “Numerical analysis of the initial conditions of fractional systems”, Communications in Nonlinear Science and Numerical Simulation, vol. 19, pp. 2935–2941, 2014.
  232. [THO 76] THOMSON W., “Mechanical integration of the general linear differential equation of any order with variable coefficients”, Proceedings of the Royal Society, vol. 24, no. 1876, pp. 271–275, 1976.
  233. [TIA 12] TIAN L.G., “Controllability and observability of impulsive fractional linear time-invariant system”, Computers and Mathematics with Applications, vol. 64, no. 10, pp. 3171–3182, 2012.
  234. [TRI 09a] TRICAUD C., CHEN Y.Q., “Solution of fractional order optimal control problems using SVD-based rational approximations”, Proceedings of the ACC’2009 Conference, St Louis, Missouri, 2009.
  235. [TRI 10a] TRICAUD C., CHEN Y.Q., “An approximated method for numerically solving fractional order optimal control problems of general form”, Computers and Mathematics with Applications, vol. 59, pp. 1644–1655, 2010.
  236. [TRI 88] TRIGEASSOU J.C., Recherche de modèles expérimentaux assistée par ordinateur, Tec et Doc Lavoisier, Paris, France, 1988.
  237. [TRI 99] TRIGEASSOU J.C., POINOT T., LIN J. et al., “Modeling and identification of a non integer order system”, ECC’99 European Control Conference, Karlsruhe, Germany, 1999.
  238. [TRI 01] TRIGEASSOU J.C., POINOT T., “Identification des systèmes à représentation continue. Application à l’estimation de paramètres physiques”, in LANDAU I.D., BESANÇON-VODA A. (eds), Identification des systèmes, Hermès, Paris, France, pp. 177–211, 2001.
  239. [TRI 09b] TRIGEASSOU J.C., MAAMRI N., “State-space modeling of fractional differential equations and the initial condition problem”, IEEE SSD’09, Djerba, Tunisia, 2009.
  240. [TRI 09c] TRIGEASSOU J.C., BENCHELLAL A., MAAMRI N. et al., “A frequency approach to the stability of Fractional Differential Equations”, Transactions on Systems, Signals and Devices, vol. 4, no. 1, pp. 1–26, 2009.
  241. [TRI 10b] TRIGEASSOU J.C., MAAMRI N., “The initial conditions of Riemman-Liouville and Caputo derivatives: an integrator interpretation”, FDA’2010 Conference, Badajoz, Spain, October 2010.
  242. [TRI 10c] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “The pseudo state space model of linear fractional differential systems”, FDA’2010 Conference, Badajoz, Spain, October 2010.
  243. [TRI 11a] TRIGEASSOU J.C, MAAMRI N., “Initial conditions and initialization of linear fractional differential equations”, Signal Processing, vol. 91, no. 3, pp. 427–436, 2011.
  244. [TRI 11b] TRIGEASSOU J.C, MAAMRI N., SABATIER J. et al., “A Lyapunov approach to the stability of fractional differentiel equations”, Signal Processing, vol. 91, no. 3, pp. 437–445, 2011.
  245. [TRI 11c] TRIGEASSOU J.C., OUSTALOUP A., “Fractional integration: a comparative analysis of fractional integrators”, IEEE SSD’11, Sousse, Tunisia, 2011.
  246. [TRI 11d] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Initialization of Riemann-Liouville and Caputo fractional derivatives”, Proceedings of IDETC/CIE FDTA’2011 Conference, Washington, DC, USA, August 2011.
  247. [TRI 11e] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Automatic Initialization of the Caputo Fractional Derivative”, CDC-ECC 2011, Orlando, USA, December 2011.
  248. [TRI 12a] TRIGEASSOU J.C., MAAMRI N., SABATIER J. et al., “Transients of fractional order integrator and derivatives”, Signal, Image and Video Processing, vol. 6, no. 3, pp. 359–372, 2012.
  249. [TRI 12b] TRIGEASSOU J.C., MAAMRI N., SABATIER J. et al., “State variables and transients of fractional order differential systems”, Computers and Mathematics with Applications, vol. 64, no. 10, pp. 3117–3140, 2012.
  250. [TRI 12c] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “State variables, initial conditions and transients of fractional order derivatives and systems”, Plenary talk, FDA’12, Nanjing, China, 2012.
  251. [TRI 13a] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “The Caputo derivative and the infinite state approach”, 6th Workshop on Fractional Differentiation and its Applications, Grenoble, France, February 2013.
  252. [TRI 13b] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Lyapunov stability of linear fractional systems. Part 1: definition of fractional energy”, ASME IDETC-CIE Conference, Portland, USA, August 2013.
  253. [TRI 13c] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Lyapunov stability of linear fractional systems. Part 2: derivation of a stability condition”, ASME IDETC-CIE Conference, Portland, USA, August 2013.
  254. [TRI 13d] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “The infinite state approach: origin and necessity”, Computers and Mathematics with Applications, vol. 66, pp. 892–907, 2013.
  255. [TRI 14] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Lyapunov stability of fractional order systems: the two derivatives case”, ICFDA’14, 23–25 June 2014.
  256. [TRI 15] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Analysis of the Caputo derivative and pseudo state representation with the infinite state approach”, in DAOU R.A.Z., MORGAN X. (eds), Fractional Calculus Theory, Nova Science Publishers, New York, USA, 2015.
  257. [TRI 16a] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Lyapunov stability of non commensurate fractional order systems: an energy balance approach”, ASME Journal of Computational and Nonlinear Dynamics, vol. 11, no. 4, p. 041007, 2016.
  258. [TRI 16b] TRIGEASSOU J.C., MAAMRI N., OUSTALOUP A., “Lyapunov stability of commensurate fractional order systems: a physical interpretation”, ASME Journal of Computational and Nonlinear Dynamics, vol. 11, no. 5, p. 051007, 2016.
  259. [TUL 93] TULLEKEN H.J.A.F., “Grey-box modeling and identification using physical knowledge and Bayesian techniques”, Automatica, vol. 29, no. 2, pp. 285–308, 1993.
  260. [VAL 07] VALERIO D., DA COSTA J.S., “Tuning rules for fractional PIDs”, in SABATIER J., AGRAWAL O.P., TENREIRO MACHADO J.A. (eds), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, New York, USA, 2007.
  261. [VAL 08] VALERIO D., ORTIGUEIRA M.D., DA COSTA J.S., “Identifying a transfer function from a frequency response”, ASME Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, 2008.
  262. [VER 08] VERGARA V., ZACKER R., “Lyapunov functions and convergence to steady state for differential equations of fractional order”, Mathematische Zeitschrift, vol. 259, pp. 287–309, 2008.
  263. [VIC 13] VICTOR S., MALTI R., GARNIER H. et al., “Parameter and differentiation order estimation in fractional models”, Automatica, vol. 49, no. 4, pp. 926–935, 2013.
  264. [VIN 00] VINAGRE B.M., PODLUBNY I., DORCAK L. et al., On Fractional PI Controllers: A Frequency Domain Approach, IFAC Workshop, Terrasa, Spain, pp. 53–58, April 2000.
  265. [WAL 97] WALTER E., PRONZATO L., Identification of Parametric Models from Experimental Data, Springer, New York, USA, 1997.
  266. [WAN 09] WANG X.Y., SONG J.M., “Synchronization of the fractional order hyper-chaos Lorentz systems with activation feedback control”, Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3351–3357, 2009.
  267. [WES 94] WESTERLUND S., EKSTAM L., “Capacitor theory”, IEEE Trans. on Dielectrics and Electrical Insulation, vol. 1, no. 5, pp. 826–839, 1994.
  268. [WIB 71] WIBERG D.M., Schaum’s Outline of Theory and Problems of State Space and Linear Systems, McGraw-Hill, New York, USA, 1971.
  269. [YUA 02] YUAN L., AGRAWAL O.P., “A numerical scheme for dynamic systems containing fractional derivatives”, Journal of Vibration and Acoustics, vol. 124, pp. 321–324, 2002.
  270. [YUA 13] YUAN J., SHI B., JI W., “Adaptive sliding mode control of a novel class of fractional chaotic systems”, Advances in Mathematical Physics, vol. 2013, article ID 576709, 2013.
  271. [YUA 18] YUAN J., ZHANG Y., LIU J. et al., “Equivalence of initialized fractional integrals and the diffusive model”, ASME Journal of Computational and Nonlinear Dynamics, vol. 13, 2018.
  272. [ZAD 08] ZADEH L.A., DESOER C.A., Linear System Theory: The State Space Approach, Dover Publications, New York, USA, 2008.
  273. [ZEM 65] ZEMANIAN A.H., Distribution Theory and Transform Analysis, McGrawHill, New York, USA, 1965.
  274. [ZHA 18] ZHAO Y., WEI Y., CHEN Y. et al., “A new look at the fractional initial value problem: the aberration phenomenon”, ASME Journal of Computational and Nonlinear Dynamics, vol. 13, no. 12, 2018.
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