A computer algorithm for the solution of the Astate equation for time-varying fractional discrete-time linear systems

• Autorzy: Kaczorek T. , Borawski K.
• Języki publikacji: EN

Abstrakty

EN

Method for finding of the solution of the state equation for time-varying fractional discrete-time linear systems is proposed and computer algorithm is presented. The effectiveness of the proposed algorithm is demonstrated on numerical examples.

Słowa kluczowe

EN

linear; time-varying; fractional; discrete-time system; state equation; solution

• Wydawca: Wydawnictwo PAK
• Czasopismo: Measurement Automation Monitoring
• Rocznik: 2015
• Tom: Vol. 61, No. 1
• Strony: 2--4
• Opis fizyczny: Bibliogr. 16 poz., rys., wykr., wzory

Twórcy

autor

Kaczorek T.

• Białystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok

autor

Borawski K.

• Białystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok

Bibliografia

• [1] Busłowicz M.: Simple analytic conditions for stability of fractional discrete-time linear systems with diagonal state matrix. Bull. Pol. Acad. of Sci., Techn. Sci., 2012, vol. 60, no. 4, pp. 809-814.
• [2] 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.
• [3] Czornik A., Nawrat 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.
• [4] Czornik A., Niezabitowski M.: Lyapunov Exponents for Systems with Unbounded Coefficients. Dynamical Systems: an International Journal, vol. 28, no. 2, 2013, 140-153.
• [5] Czornik A., Nawrat 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.
• [6] Czornik A., Niezabitowski M.: On the stability of Lyapunov exponents of discrete linear system. Proc. of European Control Conf., Zurich, 2013, 2210-2213.
• [7] Czornik A., Klamka J., Niezabitowski M.: On the set of Perron exponents of discrete linear systems, Proc. of World Congress of the 19th Int. Federation of Automatic Control, Kapsztad, 2014, 11740-11742.
• [8] Kaczorek T.: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems, vol. 58, no. 6, 2011, 1203-1210.
• [9] Kaczorek T.: Positivity and stability of time-varying discrete-time linear systems. Submitted to Conf. Transcomp 2015.
• [10] Kaczorek T.: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
• [11] Oldham K. B., Spanier J.: The Fractional Calculus. Academic Press, New York and London 1974.
• [12] Ostalczyk P.: Zarys rachunku różniczkowo-całkowego ułamkowych rzędów. Teoria i zastosowania w automatyce. Wyd. Pol. Łódzkiej, Łódź 2008.
• [13] Podlubny I.: Fractional Differential Equations. San Diego: Academic Press, 1999.
• [14] 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 Trans., vol. 53, 2014, 1081-1086.
• [15] 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.
• [16] Zhong Q., Cheng J., Zhong S.: Finite-time H control of a switched discrete-time system with average dwell time. Advances in Difference Equations, vol. 191, 2013.