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Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.
Słowa kluczowe
Rocznik
Strony
667--681
Opis fizyczny
Bibliogr. 26 poz., rys., wykr., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] A. Berman and R. J. Plemmons: Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
  • [2] K. Borawski: Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review, 93(11), (2017), 176–180.
  • [3] M. Busłowicz and T. Kaczorek: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Applied Mathematics and Computer Science, 19(2), (2009), 263–169.
  • [4] L. Farina and S. Rinaldi: Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [5] T. Kaczorek: Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [6] T. Kaczorek: Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences, Technical Sciences, 58(3), (2010), 453–458.
  • [7] T. Kaczorek: Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. on Circuits and Systems, 58(7), (2011), 1203–1210.
  • [8] T. Kaczorek: Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
  • [9] T. Kaczorek: Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences, Technical Sciences, 60(1), (2012), 9–12.
  • [10] T. Kaczorek: Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering, 5(1), (2015), 11–16.
  • [11] T. Kaczorek: Stability of fractional positive nonlinear systems, Archives of Control Sciences, 25(4), (2015), 491–496.
  • [12] T. Kaczorek: Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bulletin of the Polish Academy of Sciences, Technical Sciences, 64(3), (2016), 491–494.
  • [13] T. Kaczorek: Superstabilization of positive linear electrical circuit by statefeedbacks, Bulletin of the Polish Academy of Sciences, Technical Sciences, 65(5), (2017), 703–708.
  • [14] T. Kaczorek: Absolute stability of a class of fractional positive nonlinear systems, Int. J. Applied Mathematics and Computer Science, 29(1), (2019), 93–98.
  • [15] T. Kaczorek: Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation, 20(5), (2019), 575–579.
  • [16] T. Kaczorek: Global stability of positive standard and fractional nonlinear feedback systems, Bulletin of the Polish Academy of Sciences, Technical Sciences, 68(2), (2020), 285–288.
  • [17] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits, Springer, Cham, 2015.
  • [18] T. Kaczorek and K. Borawski: Stability of positive nonlinear systems, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2017), 564–569.
  • [19] A. M. Lyapunov: General problem of stable movement, Gostechizdat, Moscow (in Russian), 1963.
  • [20] H. Leipholz: Stability Theory, New York Academic Press, 1970.
  • [21] P. Ostalczyk: Discrete Fractional Calculus, World Scientific, River Edge, NJ, 2016.
  • [22] I. Podlubny: Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [23] A. Ruszewski: Stability of discrete-time fractional linear systems with delays, Archives of Control Sciences, 29(3), (2019), 549–567.
  • [24] A. Ruszewski: Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems, Bulletin of the Polish Academy of Sciences, Technical Sciences, 67(3), (2019), 509–515.
  • [25] Ł. Sajewski: Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2017), 482–487.
  • [26] Ł. Sajewski: 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), (2017), 709–714.
Uwagi
This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b9732ef4-eb2c-4330-af3c-8ae7ed2aee25
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