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Aström K. J., 2000, Model Uncertainty and Robust Control, COSY project.
Bayat F. M. and Afshar M., 2008, Extending the root-locus method to fractional-order systems, Journal of Applied Mathematics, Article ID 528934.
Bode H. W., 1949, Network Analysis and Feedback Amplifier Design, Tung Hwa Book Company, Shanghai.
Caponetto R., Dongola G., Fortuna L. and Petráš I., 2010, Fractional Order Systems: Modeling and Control Applications, World Scientific, Singapore.
Chen Y. Q., 2006, Ubiquitous Fractional Order Controls? Proc. of the Second IFAC Symposium on Fractional Derivatives and Applications (IFAC FDA06), July 19–21, Porto, Portugal.
Chen Y. Q., Petráš I. and Vinagre B. M., 2001, A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus, http://people.tuke.sk/ivo.petras/foc laplace.pdf.
Chen Y. Q., Bhaskaran T. and Xue D., 2008, Practical tuning rule development for fractional order proportional and integral controllers, ASME Journal of Computational and Nonlinear Dynamics, 3, 021403-1–021403-8.
Chen Y. Q., Petráš I. and Xue D., 2009, Fractional order control-A tutorial, Proc. of the American Control Conference, ACC 2009., June 10–12, 2009, St. Louis, USA, 1397–1411.
Dorčák Ľ, Petráš I., Koštial I. and Terpák J., 2002, Fractional-order state space models, Proc. of the International Carpathian Control Conference, Malenovice, Czech republic, May 27–30, 193–198.
Dorf R. C. and Bishop R. H., 1990, Modern Control Systems, Addison-Wesley, New York.
Gorenflo R., Luchko Yu. and Rogosin S., 2004, Mittag-Leffler type functions: notes on growth properties and distribution of zeros, Preprint No. A-97-04, Fachbereich Mathematik und Informatik, Freie Universitat Berlin, Germany.
LePage W. R., 1961, Complex Variables and the Laplace Transform for Engineers, McGraw-Hill, New York.
Lurie B. J., 1994, Three-Parameter Tunable Tilt-Integral-Derivative (TID) Controller, United States Patent, 5 371 670, USA.
Magin R. L., Feng X. and Baleanu D., 2009, Solving the fractional order Bloch equation, Concepts in Magnetic Resonance Part A, 34A, 16–23.
Manabe S., 1961, The non-integer integral and its application to control systems, ETJ of Japan, 6, 83–87.
Matignon D., 1998, Generalized fractional differential and difference equations: stability properties and modelling issues, Proc. of the Math. Theory of Networks and Systems Symposium, Padova, Italy.
Matignon D. and D’Andrea-Novel B., 1996, Some results on controllability and observability of finite-dimensional fractional differential systems, Computational Engineering in Systems Applications, Lille, France, IMACS, IEEE-SMC, 2, 952–956.
Monje C. A., Vinagre B. M., Feliu V. and Chen Y. Q., 2008, Tuning and auto-tuning of fractional order controllers for industry application, Contr. Eng. Pract., 16, 798–812.
Oustaloup A., 1983, Syst`emes Asservis Linéaires d’Ordre Fractionnaire: Théorie et Pratique, Editions Masson, Paris.
Oustaloup A., 1995, La Derivation Non Entiere: Theorie, Synthese et Applications, Hermes, Paris.
Oustaloup A., Mathieu B. and Lanusse P., 1995, The CRONE control of resonant plants: application to a flexible transmission, European Journal of Control, 1, 113–121.
Oustaloup A., Moreau X. and Nouillant M., 1996, The CRONE suspension, Control Engineering Practice, 4, 1101–1108.
Petráš I., 1999, The fractional-order controllers: methods for their synthesis and application, Journal of Electrical Engineering, 50, 284–288.
Petráš I. and Dorčák Ľ., 1999, The frequency method for stability investigation of fractional control systems, Journal of SACTA, 2, 75–85.
Petráš I., Dorčák Ľ., O’Leary P., Vinagre B. M. and Podlubny I., 2000, The modelling and analysis of fractional-order control systems in frequency domain, Proc. of the ICCC’2000 Conference, May 23–26, High Tatras, 261–264.
Petráš I., Podlubny I., O’Leary P., Dorčák Ľ. and Vinagre B. M., 2002, Analogue Realization of Fractional Order Controllers, Faculty of BERG, Technical University of Kosice.
Petráš I. and Dorčák Ľ., 2003, Fractional-order control systems: Modelling and simulation, Fractional Calculus and Applied Analysis, 6, 205–232.
Podlubny I., 1999a, Fractional Differential Equations, Academic Press, San Diego.
Podlubny I., 1999b, Fractional-order systems and PI γ D μ-controllers, IEEE Transactions on Automatic Control, 44, 208–213.
Podlubny I., Petráš, I., Vinagre, B.M., O’Leary P. and Dorčák Ľ., 2002, Analogue realizations of fractional-order controllers, Nonlinear Dynamics, 29, 281–296.
Raynaud H. F. and Zergaïnoh A., 2000, State-space representation for fractional order controllers, Automatica, 36, 1017–1021.
Tustin A., Allanson J. T., Layton J. M. and Jakeways R. J., 1958, The design of systems for automatic control of the position of massive objects, The Proceedings of the Institution of Electrical Engineers, 105C.
Vinagre B. M., Podlubny I., Hernandez A., and Feliu V., 2000, On realization of fractional-order controllers, Proc. of the Conference Internationale Francophone d’Automatique, Lille, Jule 5–8, 945–950.
Xue D. and Chen Y. Q., 2002, A comparative introduction of four fractional order controllers, Proc. of the 4th World Congress on Intelligent Control and Automation, June 10–14, Shanghai, China.
Yang C. and Liu F., 2006, A computationally effective predictor-corrector method for simulating fractional order dynamical control system, Australian and New Zealand Industrial and Applied Mathematics Journal, 47, C168–C184.
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Petráš, I. (2011). Fractional-Order Systems. In: Fractional-Order Nonlinear Systems. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18101-6_3
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