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Global Stability of Different Fractional Orders Multi Input Multi Output Nonlinear Feedback Systems with Interval Matrices of Positive Linear Parts

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Języki publikacji
EN
Abstrakty
EN
The global stability of continuous-time fractional orders multi–input multi-output nonlinear feedback systems with interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of these class of positive nonlinear systems are established. A procedure for computation of gain matrix characterizing the class of nonlinear elements is given and illustrated on simple example.
Twórcy
  • Bialystok University of Technology, Białystok, Poland
  • Bialystok University of Technology, Białystok, Poland
Bibliografia
  • [1] Berman A.; Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
  • [2] Borawski K. Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review, vol. 93, no. 11, 2017, 176-180.
  • [3] Busłowicz M.; Kaczorek T. Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, 2009, 263-169.
  • [4] Farina L.; Rinaldi S. Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
  • [5] Kaczorek T. Absolute stability of a class of fractional positive nonlinear systems, Int. J. Appl. Math. Comput. Sci., 2019, vol. 29, no. 1, 93-98.
  • [6] Kaczorek T. Analysis of positivity and stability of discretetime and continuous-time nonlinear systems, Computational Problems of Electrical Engineering, vol. 5, no. 1, 2015, 11-16.
  • [7] Kaczorek T. Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bull. Pol. Acad. Sci. Techn., vol. 64, no. 3, 2016, 491-494.
  • [8] Kaczorek T. Global Stability of Nonlinear Feedback Systems with Positive Linear Parts. International Journal of Nonlinear Sciences and Numerical Simulation, vol. 20, no.5, 2019, 575–579.
  • [9] Kaczorek T. Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [10] Kaczorek T. Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, 2010, 453-458.
  • [11] Kaczorek T. Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, 2011, 1203-1210.
  • [12] Kaczorek T. Positive fractional continuous-time linear systems with singular pencils, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, 2012, 9-12.
  • [13] Kaczorek T. Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
  • [14] Kaczorek T. Stability of fractional positive nonlinear systems, Archives of Control Sciences, vol. 25, no. 4, 2015, 491-496.
  • [15] Kaczorek T. Global stability of positive standard and fractional nonlinear feedback systems, Bull. Pol. Acad. Sci. Techn. vol. 68, no. 2, 2020, 285-288.
  • [16] Kaczorek T. Superstabilization of positive linear electrical circuit by state-feedbacks, Bull. Pol. Acad. Sci. Techn., vol. 65, no. 5, 2017, 703-708.
  • [17] Kaczorek T.; Borawski K. Stability of Positive Nonlinear Systems, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland 2017.
  • [18] Kaczorek T.; Rogowski K. Fractional Linear Systems and Electrical Circuits, Springer, Cham 2015.
  • [19] Lyapunov A.M. Obscaja zadaca ob ustoicivosti dvizenija, Gostechizdat, Moskwa, 1963.
  • [20] Leipholz H. Stability Theory, New York Academic Press, 1970.
  • [21] Mitkowski W. Dynamical properties of Metzler systems, Bull. Pol. Acad. Sci. Techn., vol. 56, no. 4, 2008, 309-312.
  • [22] Ostalczyk P. Discrete Fractional Calculus, World Scientific, River Edgle, NJ 2016.
  • [23] Podlubny I. Fractional Differential Equations, Academic Press, San Diego 1999.
  • [24] Ruszewski A. Stability of discrete-time fractional linear systems with delays, Archives of Control Sciences, vol. 29, no. 3, 2019, 549-567.
  • [25] Ruszewski A. Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems, Bull. Pol. Acad. Sci. Techn., vol. 67, no. 3, 2019, 509-515.
  • [26] Sajewski Ł. 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.
  • [27] Sajewski Ł. Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller, Bull. Pol. Acad. Sci. Techn., vol. 65, no. 5, 2017, 709-714.
Uwagi
1. Pełne imiona podano na stronie internetowej czasopisma w "Authors in other databases."
2. Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-91a01e45-f0d4-4ebe-9997-1b62cdf7d95f
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