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Global stability of positive discrete-time time-varying nonlinear feedback systems

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EN
Abstrakty
EN
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
Twórcy
  • Politechnika Białostocka, Wydział Elektryczny, Wiejska 45A, 15-351 Białystok, Polska
  • Politechnika Białostocka, Wydział Elektryczny, Wiejska 45A, 15-351 Białystok, Polska
Bibliografia
  • [1] Berman A., Plemmons R.J. (1994) Nonnegative Matrices in the Mathematical Sciences, SIAM.
  • [2] Borawski K. (2017) Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review, vol. 93, no. 11, 176-180.
  • [3] Busłowicz M., Kaczorek T. (2009) Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, 263-169.
  • [4] Farina L., Rinaldi S. (2000) Positive Linear Systems; Theory and Applications, J. Wiley, New York.
  • [5] Kaczorek T. (2019) Absolute stability of a class of fractional positive nonlinear systems, Int. J. Appl. Math. Comput. Sci., vol.29, no.1, 93-98.
  • [6] Kaczorek T. (2016) Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bull. Pol. Acad. Sci. Techn., vol. 64, no. 3, 491-494.
  • [7] Kaczorek T. (2002) Positive 1D and 2D Systems, Springer-Verlag, London.
  • [8] Kaczorek T. (2011) Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, 1203-1210.
  • [9] Kaczorek T. (2012) Positive fractional continuous-time linear systems with singular pencils, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, 9-12.
  • [10] Kaczorek T. (2011) Selected Problems of Fractional Systems Theory, Springer, Berlin.
  • [11] Kaczorek T. (2015) Stability of fractional positive nonlinear systems, Archives of Control Sciences, vol. 25, no. 4, 491-496.
  • [12] Kaczorek T. (2020) Global stability of positive standard and fractional nonlinear feedback systems, Bull. Pol. Acad. Sci. Techn. ,vol. 68, no. 2, 285-288.
  • [13] Kaczorek T.: Global stability of positive time-varying nonlinear feedback systems, in Press.
  • [14] Kaczorek T., Borawski K. (2017) Stability of Positive Nonlinear Systems, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland.
  • [15] Kaczorek T., Rogowski K. (2015) Fractional Linear Systems and Electrical Circuits, Springer, Cham.
  • [16] Leipholz H. (1970) Stability Theory, New York Academic Press.
  • [17] Mitkowski W. (2008) Dynamical properties of Metzler systems, Bull. Pol. Acad. Sci. Techn., vol. 56, no. 4, 309-312.
  • [18] Ruszewski A. (2014) Practical stability and asymptotic stability of interval fractional discrete-time linear state-space system, In: Szewczyk R., et al. (eds.) Recent Advances in Automation, Robotics and Measuring Techniques. Advances in Intelligent Systems and Computing, vol. 267, pp. 217–227, Heidelberg, Springer.
  • [19] Ruszewski A. (2017) Robust stability of a class of an uncertain fractional discrete-time linear state-space system, In: Szewczyk R., et al. (eds.) Innovations in Automation, Robotics and Measurement Techniques. Advances in Intelligent Systems and Computing, vol. 550, pp. 195–203, Cham, Springer, DOI:10.1007/978-3-319-54042-9_18
  • [20] Sajewski Ł. (2017) Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland, 482-487.
  • [21] Sajewslki Ł. (2017) 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, 709-714 .
  • [22] Kaczorek T. (2015) Positivity and Stability of Time-Varying Discrete-Time Linear Systems. In: Nguyen N., Trawiński B., Kosala R. (eds) Intelligent Information and Database Systems. ACIIDS 2015. Lecture Notes in Computer Science, vol 9011. Springer, Cham, pp 295-303.
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Bibliografia
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