Descriptor fractional linear systems with regular pencils

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

Słowa kluczowe

EN

descriptor system; fractional system; regular pencil

PL

układ deskrypcyjny; układ ułamkowy; pęk regularny

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: Vol. 23, no. 2
• Strony: 309--315
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267–1292.
• [2] Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
• [3] Fahmy, M.H and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421–1431.
• [4] Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.
• [5] Kaczorek, T. (2012a). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1–14.
• [6] Kaczorek, T. (2012b). Positive fractional continuous-time linear systems with singular pencils, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(1): 9–12.
• [7] Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203–1210.
• [8] Kaczorek, T. (2011b). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin.
• [9] Kaczorek, T. (2010a). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453–458.
• [10] Kaczorek, T. (2010b). Practical stability and asymptotic stability of positive fractional 2D linear systems, Asian Journal of Control 12(2): 200–207.
• [11] Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223–228, DOI: 10.2478/v10006-008-0020-0.
• [12] Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London.
• [13] Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47–57.
• [14] Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedbacks for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19–23.
• [15] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York, NY.
• [16] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653–658.
• [17] Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14: 473–480.
• [18] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
• [19] Wang, C. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197–206.
• [20] Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103–140.
• [21] Yan L., YangQuan C., Hyo-Sung A., (2011c). Fractional-order iterative learning control for fractional-order systems, Asian Journal of Control 13(1): 54–63.