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Positivity and stability of time-varying fractional discrete-time linear systems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Necessary and sufficient conditions for the positivity of time-varying fractional discrete-time linear systems are established. The problem of asymptotic stability of the positive time-varying fractional discrete-time linear systems is analyzed and sufficient conditions are given. Considerations are illustrated by numerical examples.
Wydawca
Rocznik
Strony
84--87
Opis fizyczny
Bibliogr. 18 poz., wykr., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok
Bibliografia
  • [1] Busłowicz M., Kaczorek. T.: Simple conditions for practical stability of positive fractional discrete-time linear systems. Int. J. Appl. Math. Comput. Sci., 2009, vol. 19, no. 2, pp. 263-269.
  • [2] Czornik A., Newrat A., Niezabitowski M., Szyda A.: On the Lyapunov and Bohl exponent of time-varying discrete linear systems. 20th Mediterranean Conf. on Control and Automation (MED), Barcelona, 2012, 194-197.
  • [3] Czornik A., Niezabitowski M.: Lyapunov Exponents for Systems with Unbounded Coefficients. Dynamical Systems: an International Journal, vol. 28, no. 2, 2013, 140-153.
  • [4] Czornik A., Newrat A., Niezabitowski M.: On the Lyapunov exponents of a class of the second-order discrete-time linear systems with bounded perturbations. Dynamical Systems: an International Journal, vol. 28, no. 4, 2013, 473-483.
  • [5] Czornik A., Niezabitowski M.: On the stability of Lyapunov exponents of discrete linear system, Proc. of European Control Conf., Zurich, 2013, 2210-2213.
  • [6] Czornik A., Klamka J., Niezabitowski M.: On the set of Perron exponents of discrete linear systems, Proc. of World Congress of the 19th International Federation of Automatic Control, Kapsztad, 2014, 11740-11742.
  • [7] Farina L., Rinaldi S.: Positive Linear Systems, Theory and Applications, J. Wiley, New York 2000.
  • [8] Kaczorek T., Borawski K.: A computer algorithm for the solution of the state equation for time-varying fractional discrete-time linear systems, Measurement Automation Monitoring, 2015, vol. 61, no. 1, pp. 2-4.
  • [9] Kaczorek T.: Positive 1D and 2D Systems, Springer-Verlag, London 2002.
  • [10] Kaczorek T.: Positivity and stability of time-varying discrete-time linear systems. Proc. Conf. Transcomp 2015.
  • [11] Kaczorek T.: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
  • [12] Kaczorek T.: Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa 1998 (in Polish).
  • [13] Klamka J.: Controllability and minimum energy control of fractional systems, Proc. of the 10th Asian Control Conference ASCC 2015, Kota Kinabalu, Malaysia.
  • [14] Oldham K. B., Spanier J.: The Fractional Calculus. Academic Press, New York and London 1974.
  • [15] Ostalczyk P.: Epitome of the Fractional Calculus: Theory and its Applications in Automatics, Publishing Department of Technical University of Łódź, Łódź 2008 (in Polish).
  • [16] Podlubny I.: Fractional Differential Equations. San Diego: Academic Press, 1999.
  • [17] Zhang H., Xie D., Zhang H., Wang G.: Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach. ISA Transactions, vol. 53, 2014, 1081-1086.
  • [18] Zhang J., Han Z., Wu H., Hung J.: Robust stabilization of discrete-time positive switched systems with uncertainties and average dwell time switching. Circuits Syst., Signal Process., vol. 33, 2014, 71-95.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b3b2bb93-6e07-48ad-8356-9b48f152572d
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