Selected publications of Ivo Petras

(Tech. Univ. of Kosice, BERG Faculty)



I. Books/Textbooks/Book chapters (10+):


  1. Petráš, I. (Ed.): Handbook of Fractional Calculus with Applications: Vol. 6: Applications in Control, De Gruyter, 2019, p. 427, ISBN 978-3-11-057174-5.
  2. Petráš, I. : Fractional-order nonlinear systems: modeling, analysis and simulation, HEP, Springer-Verlag, 2011, p. 218. ISBN 978-3-642-18100-9.
  3. Caponetto, R., Dongola, G., Fortuna, L., and Petráš, I.: Fractional Order Systems: Modelling and Control Applications, World Scientific Publishing, 2010, p.178. ISBN 978-981-4304-19-1.
  4. Petráš, I.: Fractional-order chaotic systems. 1. vyd. Košice: Reprocentrum  (Digital Print Hause), 2009. p. 126, ISBN 978-80-553-0112-9.
  5. Petráš, I., Podlubny, I., O'Leary, P., Dorčák, Ľ., Vinagre, B.M.: Analog Realizations of Fractional Order Controllers, TU Košice, 2002, p. 84, ISBN 80-7099-627-7.
  6. Petráš, I.: Modified versions of the fractional-order PID controller. In: Handbook of Fractional Calculus with Applications: Vol. 6: Applications in Control, De Gruyter, 2019, p. 427, pp. 57-72, ISBN 978-3-11-057174-5.
  7. Petráš, I. : Fractional derivatives, fractional integrals, and fractional differential equations in Matlab, In: A. Assi Eds. Engineering Education and Research Using MATLAB, InTech, 2011, ISBN 978-953-307-656-0, chapter 10.
  8. Petráš, I., Chen, Y.Q., Vinagre, B.M.:  Robust stability test for interval fractional order linear systems. In: V. Blondel and A. Megretski Eds. Unsolved problems in mathematics  and control systems, Princeton University Press, USA, 2004. ISBN 0-691-11748-9.
  9. Petráš, I., Hypiusová, M.: Design of fractional - order controllers via H∞ norm minimisation, In: J. Mikleš and V. Veselý Eds. Selected Topics in Modeling and Control, vol. 3, 2002, pp. 50–54, STU Press Bratislava, ISBN 80-227-1815-7.



II. Journal papers (60+):


  1. Petráš, I.: Novel Generalized Low-Pass Filter with Adjustable Parameters of Exponential-Type Forgetting and Its Application to ECG Signal, Sensors, vol. 22, 2022.
  2. Petráš, I.: Novel Fractional-Order Model Predictive Control: State-Space Approach, IEEE Access, vol. 9, 2021, pp. 92769-92775.
  3. Petráš, I.,  Terpák, J.: Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry, Mathematics,  vol. 7, no. 6, 2019.
  4. Gonzalez, E., Petráš, I., Ortigueira, M.D.: Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance, Fractional Calculus and Applied Analysis, vol. 21, no. 3, 2018, pp. 613-627.
  5. Dimeas, I., Petráš, I., Psychalinos, C.: New analog implementation technique for fractional-order controller: A DC motor control, AEU - International Journal of Electronics and Communications, vol. 78, 2017, pp. 192-200.
  6. Tepljakov, A., Gonzalez, E. A., Petlenkov, E., Belikov, J., Monje, C. A, Petráš, I.: Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop, ISA Transactions, vol. 60, 2016, pp. 262-273.
  7. Sierociuk, D., Škovránek, T., Macias, M., Podlubny, I., Petráš, I., Dzielinski, A., Ziubinski, P.: Diffusion process modeling by using fractional-order models, Applied Mathematics and Computation, vol. 257, 2015, pp. 2- 11.
  8. Sierociuk, D., Podlubny, I., Petráš, I.: Experimental Evidence of Variable-Order Behavior of Ladders and Nested Ladders, IEEE Transactions on Control Systems Technology, vol. 21, no. 2, 2013, pp. 459-466.
  9. Petráš, I., Sierociuk, D.; Podlubny, I.: Identification of parameters of a half-order system, IEEE Transactions on Signal Processing, vol. 60, no.10, 2012, pp. 5561-5566.
  10. Baleanu, D., Asad, J.H., Petráš, I.:  Fractional-order two-electric pendulum, Romanian Reports in Physics, vol. 64, no. 4, 2012, pp. 907-914.
  11. Petráš, I.: Tuning and implementation methods for fractional-order controllers, Fractional Calculus and Applied Analysis, vol. 5, no.2, 2012, pp. 282-303.
  12. Škovránek, T., Podlubny, I., Petráš, I.: Modeling of the national economies in state-space: A fractional calculus approach, Economic Modelling, vol. 29, no. 4, 2012, pp. 1322-1327.
  13. Petráš, I.: Chaos in Fractional-order Population Model, International Journal of Bifurcation and Chaos  in Applied Sciences and Engineering, vol. 22, no. 4, 2012.
  14. Baleanu, D.,  Petráš, I., Asad, J.H., Velasco M.P.: Fractional Pais–Uhlenbeck Oscillator, International Journal of Theoretical Physics, vol. 51, no. 4, 2012, pp. 1253-1258.
  15. Petráš, I., Magin, R.: Simulation of drug uptake in a two compartmental fractional model for a biological system, Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 12, 2011, pp. 4588-4595.
  16. Petráš, I.: An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications. Advances in Difference Equations, vol. 2011, p. 1-14.
  17. Petráš, I., Bednárová, D.: Control Of Fractional-Order Nonlinear Systems: A Review, Acta Mechanica et Automatica, vol. 5 no.2, 2011, pp. 96-100.
  18. Petráš, I.:  Modeling and numerical analysis of fractional-order Bloch equations, Computers & Mathematics with Applications, vol. 61, no. 2, 2011, pp. 341-356.
  19. Petráš, I.: Fractional-order memristor-based Chua's circuit. IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 57, no. 12, 2010, pp. 975-979.
  20. Petráš, I., Podlubný, I.: Least squares or least circles?: A comparison of classical regression and orthogonal. Chance, vol. 23, no. 2, 2010, pp. 38-42.
  21. Petráš, I., Bednárová, D.: Total least squares approach to modeling: A Matlab toolbox, Acta Montanistica Slovaca, vol. 15, no. 2, 2010, pp. 158-170.
  22. Petráš, I.: Discussion on: “Simple fractional order model structures and their applications in control system design“, European Journal of Control, vol. 16, no. 6, 2010, pp. 697-698.
  23. Petráš, I.: A note on the fractional-order Volta's system. Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 2, 2010, pp. 384-393,
  24. Petráš, I.: Stability of fractional order systems with rational orders: A survey. Fractional Calculus and Applied Analysis, vol. 12, no. 3, 2009, pp. 269-298.
  25. Petráš, I.: Fractional-order feedback control of a DC motor. Journal of Electrical Engineering. vol. 60, no. 3, 2009, pp. 117-128.
  26. Petráš, I., Podlubny, I.: State space description of national economies: The V4 countries, Computational Statistics & Data Analysis, vol. 52, 2007, pp. 1223-1233.
  27. Petráš, I.: Chaos in the fractional-order Volta's system: modeling and simulation.  Nonlinear Dynamics, vol.57, no. 1-2, 2009, pp. 157-170.
  28. Petráš, I.: A note on the fractional-order Chua’s system.  Chaos, Solitons & Fractals, vol. 38, no.1, 2008, pp. 140-147.
  29. Petráš, I., Bednárová D., Podlubný I.: Description of behavior of national economies in state space, Acta Montanistica Slovaca, vol. 13, no. 1, 2008, pp. 183-186.
  30. Dorčák, Ľ., Terpák, J., Petráš, I., Dorčáková, F.: Electronic realization of the fractional-order systems. Acta Montanistica Slovaca, vol. 12, no. 3, 2007, pp. 231-237.
  31. Petráš, I.: Method for simulation of the fractional order chaotic systems, Acta Montanistica Slovaca, vol. 11, no. 4, 2006, pp. 273 – 277.
  32. Vinagre, B. M, Chen, Y.Q., Petráš, I.: Two Direct Tustin Discretization Methods for Fractional-Order Differentiator/Integrator, Journal of The Franklin Institute, vol. 340, no.5, 2003, pp. 349 – 362.
  33. Petráš, I., Dorčák, Ľ.: Fractional-Order Control Systems: Modelling and Simulation, Fractional Calculus and Applied Analysis, vol. 6, no. 2, 2003, pp. 205 - 232.
  34. Podlubny, I., Petráš, I., Vinagre, B.M., Chen, Y.Q., O’Leary P., Dorčák, Ľ.: Realization of fractional order controllers, Acta Montanistica Slovaca, vol. 8, no. 4, 2003, pp. 233 – 235.
  35. Podlubny, I., Petráš, I., Vinagre, B.M., O'Leary, P., Dorčák, Ľ.: Analogue  Realization of Fractional-Order Controllers. Nonlinear Dynamics, vol. 29, no. 1-4, 2002, pp. 281-296.
  36. Vinagre, B. M, Petráš, I., Podlubny, I., Chen, Y.Q.: Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control. Nonlinear Dynamics, vol. 29, no. 1 - 4, 2002, pp. 269-279.
  37. Petráš, I.: Control of fractional-order Chua's system, Journal of Electrical Engineering, vol. 53, no. 7-8, 2002, Bratislava, pp. 219 - 222.
  38. Petráš, I., Vinagre, B. M.: Practical application of digital fractional-order controller to temperature control, Acta Montanistica Slovaca, vol. 7, no.2, 2002, pp. 131-137.
  39. Koštial, I., Nemčovský, P., Dorčák, Ľ., Terpák, J., Petráš, I., Rogaľ, M., Halmo, M.: Real time blast furnace modeling, Metallurgy, vol. 40, no. 3, 2001, pp. 147-150.
  40. Petráš, I., Dorčák, Ľ.: The frequency method for stability investigation of fractional control systems, Journal of SACTA, vol. 2, no. 1-2, 1999, pp.75 - 85.
  41. Petráš, I.: The fractional - order controllers: Methods for their synthesis and application, Journal of Electrical Engineering, vol. 50, no. 9 - 10, 1999, pp. 284 - 288.
  42. Petráš, I., Dorčák, Ľ., Koštial, I.: Control quality enhancement by fractional-order controllers, Acta Montanistica Slovaca, vol. 2, no. 2, 1998, pp. 143 – 148.



III. Conference papers (90+):


  1. Petráš, I.: Tuning of the non-linear fractional-order controller, In: Proc. of the 2019 20th IEEE International Carpathian Control Conference (ICCC), Kraków-Wieliczka, Poland, May 26-29, 2019, pp. 1-4.
  2. Tepljakov, A., Petlenkov, E., Gonzalez, E. A., Petráš, I.: Design of a MATLAB-based teaching tool in introductory fractional-order systems and controls, In: Proc. of the IEEE Frontiers in Education Conference (FIE), Indianapolis, USA, 18-21 Oct. 2017.
  3. Gonzalez, E. A., Petráš, I.: Advances in Fractional Calculus: Control and Signal Processing Applications, In: Proc. of the 2015 16th IEEE International Carpathian Control Conference (ICCC), Szilvásvárad, Hungary, May 27-30, 2015, pp. 147-152.
  4. Petráš, I.: Practical aspects for implementation of fractional-order controllers, In: Proc. of the 2014 15th IEEE International Carpathian Control Conference (ICCC), Velké Karlovice, Czech Republic, May 28-30, 2014, pp. 428-431.
  5. Podlubny, I., Petráš, I., Škovránek, T.: Fitting of experimental data using Mittag-Leffler function, In: Proc. of the 2012 13th IEEE International Carpathian Control Conference (ICCC), May 28-31, 2012, High Tatras, Slovak Republic, pp. 578-581.
  6. Petráš, I., Chen, Y.Q.: Fractional-order circuit elements with memory, In: Proc. of the 2012 13th IEEE International Carpathian Control Conference (ICCC), May 28-31, 2012, High Tatras, Slovak Republic, pp. 552-558.
  7. Petráš, I.: Practical Aspects of Tuning and Implementation of Fractional-Order Controllers, In: Proc. of the MESA-1 The Fifth Symposium on Fractional Derivatives and Their Applications (FDTA’11), ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications (MESA’11), August 28-31, 2011, Washington, DC., USA, DETC2011-47053.
  8. Sierociuk, D., Petráš, I.: Modeling of Heat Transfer Process by Using Discrete Fractional-Order Neural Networks, In: Proc. of the 16th Int. Conf. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, August 22-25, 2011.
  9. Záhorčák, G., Petráš, I.: Control system of mobile robot. In: ICCC 2011 Proceedings of the 12th International Carpatian Control Conference: 25-28 May 2011, Velké Karlovice, Czech Republic. - S.l.: IEEE, 2011 pp. 473-477.
  10. Petráš, I.: Fractional-order biological system model: A case of two-predators and one-prey. In: FDA’10 Proceedings of the 4th IFAC Workshop on Fractional Differentiation and Its Applications, Badajoz, Spain, October 18-20, 2010.
  11. Petráš, I., Chen, Y.Q., Coopmans, C.: Fractional-order memristive systems. In: ETFA 2009: 14th International Conference on Emerging Technologies and Factory Automation: September 22-26, 2009, Mallorca, Spain. S.l.: IEEE, 2009. pp. 1-8.
  12. Chen, Y.Q:, Petráš, I., Xue, D.: Fractional order control - A tutorial. In: American Control Conference: St.Louis, Missouri, USA, June 10 - 12, 2009. pp. 1397-1411.
  13. Podlubný, I., Škovránek, T., Bednárová, D., Petráš, I.: State space description of national economies: the Scandinavian countries. In: Information sciences 2007: Proceedings of the 10th Joint Conference: Salt Lake City, Utah, USA, 18 - 24 July 2007. S.l.: World Scientific Publishing, 2007.
  14. Petráš, I.:  A Note on the Fractional-Order Cellular Neural Networks, Proc. of the IEEE World Congress on Computational Intelligence, International Joint Conference on Neural Networks, Vancouver, Canada, July 16 -21, 2006, pp. 2000 – 2003.
  15. Petráš, I., Chen, Y.Q., Vinagre, B.M., Podlubny, I.: Stability of Linear Time Invariant Systems with Interval fractional Order and Interval Coefficients, In: Proc. of the second IEEE International Conference on Computational Cybernetics, Vienna, August 30 – September 1, 2004, pp. 341-346.
  16. Petráš, I., Chen, Y.Q., Vinagre, B. M.: A Robust Stability Test Procedure for a Class of Uncertain LTI Fractional-Order Systems, In: Proc. of the ICCC'2002, Malenovice, Czech Republic, May 27 - 30, 2002, pp. 247 – 252.
  17. Terpák, J., Dorčák, Ľ., Koštial, I., Petráš, I.: A simulation model for blast furnace operation, In: Proceedings of Process Control 2002, Kouty nad Desnou, Czech Republic, June 9 - 12, 2002, pp. R145 -1-8.
  18. Vinagre, B.M., Petráš, I., Podlubny, I., Chen, Y.Q.: Stability of fractional-order model reference adaptive control, In: Proc. of the MTNS'2002, August 12 - 16, 2002, Notre Dame, USA. pp. 118 – 121.
  19. Vinagre, B. M., Petráš, I., Merchan P., Dorčák, Ľ.: Two digital realizations of fractional controllers: Application to temperature control of a solid, In: Proc. of the ECC'2001, September 4-7, Seminario de Vilar, Porto, Portugal, pp.1764 - 1767.
  20. Petráš, I., Dorčák, Ľ., Terpák, J., Koštial, I.: Fractional-order control systems, In: Proceedings of the 3rd DAAAM Workshop "Intelligent Manufacturing Systems", 29th     November 2001, Košice, pp. 61-62.
  21. Koštial, I., Nemčovský, P., Rogaľ, M., Terpák, J., Dorčák, Ľ., Petráš, I .: Blast furnace process control, In: Proc. of IFAC Workshop, Future trends in Automation in Mineral and Metal Processing, August 22-24, 2000, Finland, pp. 263 – 268.



Web publications (10+):


  1. Chen, Y.Q, Petráš, I., Vinagre, B.M.: A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus, 2001, url:
  2. Petráš, I.: Stability of fractional-order systems with rational orders, Arxiv preprint arXiv:0811.4102, 2008.
  3. Sierociuk, D.,  Podlubny, I.,  Petráš, I.: Experimental evidence of variable-order behavior of ladders and nested ladders, Arxiv preprint arXiv:1107.2575, 2011.