Have a personal or library account? Click to login
On The Global Stability of Fractional Feedback Nonlinear Systems with Interval Matrices of Positive Linear Parts and Application to Electrical Circuits Cover

On The Global Stability of Fractional Feedback Nonlinear Systems with Interval Matrices of Positive Linear Parts and Application to Electrical Circuits

Open Access
|Mar 2026

References

  1. Berman, A. and Plemmons, R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia.
  2. Borawski, K. (2017a). Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review 93(11): 176–180.
  3. Borawski, K. (2017b). Stability of positive nonlinear systems, 22nd International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 564–569.
  4. Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263–169, DOI: 10.2478/v10006-009-0022-6.
  5. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York.
  6. Kaczorek, T. (2020). Global stability of positive standard and fractional nonlinear feedback systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 30(2).
  7. Kaczorek, T. (2019a). Absolute stability of a class of fractional positive nonlinear systems, International Journal of Applied Mathematics and Computer Science 29(1): 93–98, DOI: 10.2478/amcs-2019-0007.
  8. Kaczorek, T. (2019b). Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation 20(5): 575–579.
  9. Kaczorek, T. (2016). Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(3): 491–494.
  10. Kaczorek, T. (2015a). Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering 5(1): 11–16.
  11. Kaczorek, T. (2015b). Stability of fractional positive nonlinear systems, Archives of Control Sciences 25(4): 491–496.
  12. Kaczorek, T. (2012). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9–12.
  13. Kaczorek, T. (2011a) Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203–1210.
  14. Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer, Berlin.
  15. Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
  16. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
  17. Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.
  18. Kharitonov, V.L. (1978). Asymptotic stability of an equilibrium position of a family of systems of differential equations, Differentsialnye urawnienia 14: 2086-2088.
  19. Lyapunov, A.M. (1963). General Problem of the Stability of Motion, Gostechizdat, Moscowa.
  20. Leipholz, H. (1970). Stability Theory, Academic Press, New York.
  21. Mitkowski, W. (2008). Dynamical properties of Metzler systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 309–312.
  22. Ostalczyk, P. (2016). Discrete Fractional Calculus, World Scientific, River Edge.
  23. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego.
  24. Ruszewski, A. (2019). Stability conditions for fractional discrete-time state-space systems with delays, 24th International Conference Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 1–7.
  25. Sajewski, L. (2017a). Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays, 22nd International Conference Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 482–487.
  26. Sajewski, L. (2017b). Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller, Bulletin of the Polish Academy of Sciences: Technical Sciences 65(5): 709–714.
  27. Sene, N. (2020). Global asymptotic stability of the fractional differential equations, Journal of Nonlinear Sciences and Applications 13(3): 171–175.
  28. Sene, N. and Srivastava, G. (2019). Generalized Mittag-Leffler input stability of the fractional differential equations, Symmetry 11(5): 608.
DOI: https://doi.org/10.61822/amcs-2026-0001 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 5 - 11
Submitted on: Jun 30, 2025
|
Accepted on: Nov 3, 2025
|
Published on: Mar 21, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2026 Tadeusz Kaczorek, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.