Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/amcs-2016-0019

• Języki publikacji: EN

Abstrakty

EN

Fractional descriptor reduced-order nonlinear observers for a class of fractional descriptor continuous-time nonlinear systems are proposed. Sufficient conditions for the existence of the observers are established. The design procedure for the observers is given and demonstrated on a numerical example.

Słowa kluczowe

EN

fractional system; descriptor system; nonlinear system; reduced order observer

PL

układ ułamkowy; układ deskryptorowy; układ nieliniowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2016
• Tom: Vol. 26, no. 2
• Strony: 277--283
• Opis fizyczny: Bibliogr. 31 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] Cuihong, W. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197–206.
• [2] Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267–1292.
• [3] Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
• [4] Fahmy, M.M. and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalue assignment, International Journal of Control 49(4): 1421–1431.
• [5] Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.
• [6] Guang-ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
• [7] Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, J. Wiley, New York, NY.
• [8] Kaczorek, T. (2001). Full-order perfect observers for continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(4).
• [9] Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedback for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19–23.
• [10] 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.
• [11] Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203–1210.
• [12] Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
• [13] Kaczorek, T. (2012a). Checking of the positivity of descriptor linear systems with singular pencils, Archive of Control Sciences 22(1): 77–86.
• [14] 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.
• [15] Kaczorek, T. (2013). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1051–1064.
• [16] Kaczorek, T. (2014a). Fractional descriptor observers for fractional descriptor continuous-time linear system, Archives of Control Sciences 24(1): 5–15.
• [17] Kaczorek, T. (2014b). Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 62(4): 889–895.
• [18] Kaczorek, T. (2015). Prefect observers of fractional descriptor continuous-time linear systems, in K.J. Latawiec et al. (Eds.), Advances in Modeling and Control of Non-integer orders Systems, Lecture Notes in Electrical Engineering, Vol. 320, Springer, Berlin/Heidelberg, pp. 5–12.
• [19] Kociszewski, R. (2013). Observer synthesis for linear discrete-time systems with different fractional orders, Pomiary Automatyka Robotyka (2): 376–381, (on CD-ROM).
• [20] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653–658.
• [21] Lewis, F.L. (1983). Descriptor systems, expanded descriptor equation and Markov parameters, IEEE Transactions on Automatic Control AC-28(5): 623–627.
• [22] Luenberger, D.G. (1977). Dynamical equations in descriptor form, IEEE Transactions on Automatic Control AC-22(3): 312–321.
• [23] Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14(5): 473–480.
• [24] Matignon, D. (1996). Stability result on fractional differential equations with applications to control processing, IMACSSMC Proceedings, Lille, France, pp. 963–968.
• [25] N’Doye I., Darouach M., Voos H. and Zasadzinski M. (2013). Design of unknown input fractional-order observers for fractional-order systems, International Journal of Applied Mathematics and Computer Science 23(3): 491–500, DOI: 10.2478/amcs-2013-0037.
• [26] Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
• [27] Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).
• [28] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
• [29] Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103–140.
• [30] Vinagre, B.M., Monje, C.A. and Calderon, A.J. (2002). Fractional order systems and fractional order control actions, Lecture 3, IEEE CDC’02, Las Vegas, NV, USA.
• [31] Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429: 2640–2659.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.