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Descriptor fractional discrete-time linear system with two different fractional orders and its solution

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EN
Abstrakty
EN
Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering, Białystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland
Bibliografia
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  • [4] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [5] T. Kaczorek, “Descriptor fractional linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23 (2), 309-315 (2013).
  • [6] T. Kaczorek, “Singular fractional continuous-time and discretetime linear systems”, Acta Mechanica et Automatica 7 (1), 26-33 (2013).
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  • [16] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differenctial Equations, Willey, New York, 1993.
  • [17] T. Kaczorek, “Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils”, Tech. Transp. Szyn. 10, 415-422 (2013).
  • [18] T. Kaczorek, “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica 5 (4), 1-5 (2011).
  • [19] T. Kaczorek, “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci. 23 (1), 29-33 (2013).
  • [20] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor continuous-time linear systems”, Bull. Pol. Ac.: Tech. 62 (3), 409-412, (2014).
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  • [23] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems 58 (6), 1203-1210 (2011).
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  • [27] Ł. Sajewski, “Solution of the state equation of descriptor fractional continuous-time linear systems with two different fractional”, Progress in Automation, Robotics and Measuring Techniques, Advances in Intelligent Systems and Computing 350, 233-242 (2015).
  • [28] Ł. Sajewski, “Descriptor fractional discrete-time linear system and its solution - comparison of three different methods”, Proc. Conf. Automation 1, (2016), (to be published).
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Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7346cd96-dfe1-4ed5-90ef-30e65369cd40
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