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Veisi, Amir, Delavari, Hadi. (1404). Stability of Nonlinear Fractional Order Discrete-Time Systems for Engineering Applications. پژوهشنامه مدیریت اجرایی, 2(4), 1-12. doi: 10.22080/cste.2025.29016.1030
Amir Veisi; Hadi Delavari. "Stability of Nonlinear Fractional Order Discrete-Time Systems for Engineering Applications". پژوهشنامه مدیریت اجرایی, 2, 4, 1404, 1-12. doi: 10.22080/cste.2025.29016.1030
Veisi, Amir, Delavari, Hadi. (1404). 'Stability of Nonlinear Fractional Order Discrete-Time Systems for Engineering Applications', پژوهشنامه مدیریت اجرایی, 2(4), pp. 1-12. doi: 10.22080/cste.2025.29016.1030
Veisi, Amir, Delavari, Hadi. Stability of Nonlinear Fractional Order Discrete-Time Systems for Engineering Applications. پژوهشنامه مدیریت اجرایی, 1404; 2(4): 1-12. doi: 10.22080/cste.2025.29016.1030

Stability of Nonlinear Fractional Order Discrete-Time Systems for Engineering Applications

Contributions of Science and Technology for Engineering
مقاله 1، دوره 2، شماره 4، آذر 2025، صفحه 1-12    اصل مقاله (1015.69 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22080/cste.2025.29016.1030
نویسندگان
Amir Veisi1؛ Hadi Delavari* 2
1Department of Electrical Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran
2Department of Electrical Engineering, Hamedan University of Technology, Hamedan, Iran
تاریخ دریافت: 25 فروردین 1404،  تاریخ بازنگری: 11 خرداد 1404،  تاریخ پذیرش: 01 تیر 1404 
چکیده
Data-driven approaches, by effectively capturing complex nonlinear behaviors, have emerged as a powerful tool for enhancing control of real engineering systems. Nonlinear discrete-time fractional-order systems have earned much interest in the design of controllers and system modeling due to special characteristics that include long-term memory, an expansion of stability domains, and higher accuracy. It is thus very important to establish some straightforward theories for proving and analyzing stability of these particular systems. This paper represents a sophisticated approach to the stability analysis of discrete Caputo fractional-order systems through the development of a new Lyapunov-based stability analysis framework tailored for such systems. The effectiveness of the proposed approach has been critically analyzed theoretically and validated through numerical simulations. Methodologically innovative, thus, such reasoning has provided one strong solution for the stability test problem of discrete fractional order systems, opening greater avenues toward advanced construction or progress of control theory and dynamical system theories within fractional calculus.
کلیدواژه‌ها
Stability Analysis؛ Discrete Caputo Fractional Order Calculus؛ Fractional Calculus؛ Control Systems؛ Lyapunov Stability
مراجع
  1. Das, S. (2011). Functional fractional calculus. Berlin: Springer. doi:10.1007/978-3-642-20545-3.
  2. Xue, D., & Bai, L. (2024). Fractional Calculus, High-Precision Algorithms and Numerical Implementations. Springer Singapore. doi:10.1007/978-981-99-2070-9.
  3. Zayed, A. I. (2024). Fractional integral transforms: Theory and applications. Chapman and Hall/CRC, Boca Raton, United States. doi:10.1201/9781003089353.
  4. Belhoste, B. (2012). Augustin-Louis Cauchy: A Biography. Springer, Cham, Switzerland.
  5. Al-Refai, M., & Luchko, Y. (2023). General Fractional Calculus Operators of Distributed Order. Axioms, 12(12), 1075. doi:10.3390/axioms12121075.
  6. Gorenflo, R., Kilbas, A. A., Mainardi, F., & Rogosin, S. (2020). Mittag-Leffler Functions, Related Topics and Applications. Springer Monographs in Mathematics. Springer, Berlin, Germany. doi:10.1007/978-3-662-61550-8.
  7. Singh, H., Srivastava, H. M., & Pandey, R. K. (2023). Special Functions in Fractional Calculus and Engineering. CRC Press, Boca Raton, United States. doi:10.1201/9781003368069.
  8. Yang, Y., & Zhang, H. H. (2019). Fractional calculus with its applications in engineering and technology. Synthesis Lectures on Mechanical Engineering, Springer, Cham, Switzerland, doi:10.1007/978-3-031-79625-8 .
  9. Ferreira, R. A. (2022). Discrete fractional calculus and fractional difference equations. SpringerBriefs in Mathematics, Springer, Cham, Switzerland. doi:10.1007/978-3-030-92724-0 .
  10. Abdeljawad, T. (2011). On Riemann and Caputo fractional differences. Computers and Mathematics with Applications, 62(3), 1602–1611. doi:10.1016/j.camwa.2011.03.036.
  11. Sebah, P., & Gourdon, X. (2002). Introduction to the gamma function. American Journal of Scientific Research, 2.
  12. Yuldashova, H., & Hasanov, A. (2024). Mittag-Leffler type functions of three variables. doi:22541/au.171604045.56900857/v1.
  13. Ostalczyk, P. (2015). Discrete Fractional Calculus: Applications in Control and Image Processing. World Scientific Publishing Company, Singapore. doi:10.1142/9833.
  14. Lubich, Ch. (1986). Discretized Fractional Calculus. SIAM Journal on Mathematical Analysis, 17(3), 704–719. doi:10.1137/0517050.
  15. Bhangale, N., Kachhia, K. B., & Gómez-Aguilar, J. F. (2023). Fractional viscoelastic models with Caputo generalized fractional derivative. Mathematical Methods in the Applied Sciences, 46(7), 7835–7846. doi:10.1002/mma.7229.
  16. Haq, S. U., Khan, M. A., Khan, Z. A., & Ali, F. (2020). MHD effects on the channel flow of a fractional viscous fluid through a porous medium: An application of the Caputo-Fabrizio time-fractional derivative. Chinese Journal of Physics, 65, 14–23. doi:10.1016/j.cjph.2020.02.014.
  17. Abro, K. A., Memon, A. A., & Uqaili, M. A. (2018). A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. European Physical Journal Plus, 133(3), 1–9. doi:10.1140/epjp/i2018-11953-8.
  18. Veisi, A., & Delavari, H. (2022). Fractional-order backstepping strategy for fractional-order model of COVID-19 outbreak. Mathematical Methods in the Applied Sciences, 45(7), 3479–3496. doi:10.1002/mma.7994.
  19. Veisi, A., Maleki, H., & Delavari, H. (2023). Adaptive Fractional Sliding Mode Controller for Controlling Airway Pressure in an Artificial Ventilation System. 2023 9th International Conference on Control, Instrumentation and Automation, ICCIA 2023. doi:10.1109/ICCIA61416.2023.10506394.
  20. Delavari, H., & Veisi, A. (2023). Fuzzy fractional-order sliding mode control of COVID-19 virus variants. Computational Intelligence in Electrical Engineering, 14(1), 93-108.
  21. Ortigueira, M. D. (2024). Principles of fractional signal processing. Digital Signal Processing, 149, 104490. doi:10.1016/j.dsp.2024.104490.
  22. Cattani, C., Srivastava, H. M., & Yang, X.-J. (Eds.). (2015). Fractional Dynamics. Walter de Gruyter, Berlin, Germany. doi:10.1515/9783110472097.
  23. Imran, M. A., Khan, I., Ahmad, M., Shah, N. A., & Nazar, M. (2017). Heat and mass transport of differential type fluid with non-integer order time-fractional Caputo derivatives. Journal of Molecular Liquids, 229, 67–75. doi:10.1016/j.molliq.2016.11.095.
  24. Delavari, H., & Veisi, A. (2021). Robust Control of a Permanent Magnet Synchronous Generators based Wind Energy Conversion. 2021 7th International Conference on Control, Instrumentation and Automation, ICCIA 2021. doi:10.1109/ICCIA52082.2021.9403590.
  25. Veisi, A., & Delavari, H. (2021). Adaptive Fractional order Control of Photovoltaic Power Generation System with Disturbance Observer. 2021 7th International Conference on Control, Instrumentation and Automation, ICCIA 2021. doi:10.1109/ICCIA52082.2021.9403598.
  26. Delavari, H., & Veisi, A. (2024). A new robust nonlinear controller for fractional model of wind turbine based DFIG with a novel disturbance observer. Energy Systems, 15(2), 827–861. doi:10.1007/s12667-023-00566-3.
  27. Veisi, A., & Delavari, H. (2024). Adaptive optimized fractional order control of doubly-fed induction generator (DFIG) based wind turbine using disturbance observer. Environmental Progress & Sustainable Energy, 43(2), 14087. doi:10.1002/ep.14087.
  28. Veisi, A., Delavari, H., & Shanaghi, F. (2023). Maximum Power Point Tracking in a Photovoltaic System by Optimized Fractional Nonlinear Controller. 2023 8th International Conference on Technology and Energy Management, ICTEM 2023. doi:10.1109/ICTEM56862.2023.10083639.
  29. Veisi, A., & Delavari, H. (2023). Adaptive fractional backstepping intelligent controller for maximum power extraction of a wind turbine system. Journal of Renewable and Sustainable Energy, 15(6). doi:10.1063/5.0161571.
  30. Chen, G. S. (2011). A generalized Young inequality and some new results on fractal space. arXiv preprint arXiv:1107.5222.
  31. Gajic, Z., & Qureshi, M. T. J. (2008). Lyapunov matrix equation in system stability and control. Courier Corporatio, Chelmsford, United States.
  32. Veisi, A., & Delavari, H. (2025). Deep reinforcement learning optimizer based novel Caputo fractional order sliding mode data driven controller. Engineering Applications of Artificial Intelligence, 140, 109725. doi:10.1016/j.engappai.2024.1097255.
  33. Veisi, A., & Delavari, H. (2024). Fractional data driven controller based on adaptive neural network optimizer. Expert Systems with Applications, 257. doi:10.1016/j.eswa.2024.125077.
  34. Fu, H., & Kao, Y. (2025). Robust sliding mode control of discrete fractional difference chaotic system. Nonlinear Dynamics, 113(2), 1419–1431. doi:10.1007/s11071-024-10279-6.
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