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Reduced-order perfect nonlinear observers of fractional descriptor discrete-time nonlinear systems

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EN
Abstrakty
EN
The purpose of this work is to propose and characterize fractional descriptor reduced-order perfect nonlinear observers for a class of fractional descriptor discrete-time nonlinear systems. Sufficient conditions for the existence of these observers are established. The design procedure of the observers is given and demonstrated on a numerical example.
Twórcy
autor
  • Faculty of Electrical Engineering, Białystok Technical University, 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.
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  • [3] Dai, L. (1989). Singular Control Systems, Springer, Berlin.
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  • [7] Kaczorek, T. (1992). Linear Control Systems, 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): 549–558.
  • [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 Transaction on Circuits and Systems 58(7): 1203–1210.
  • [12] Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer, Berlin.
  • [13] Kaczorek, T. (2012a). Checking of the positivity of descriptor linear systems with singular pencils, Archives 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 systems, Archives of Control Sciences 24(1): 27–37.
  • [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). Perfect observers of fractional descriptor continuous-time linear systems, in K. Latawiec, et al. (Eds.), Advances in Modeling and Control of Non-integer Orders Systems, Springer, Cham, pp. 3–12.
  • [19] Kaczorek, T. (2016a). Perfect nonlinear observers of descriptor discrete-time nonlinear systems, Asian Journal of Control, (submitted).
  • [20] Kaczorek, T. (2016b). Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems, Fractional Calculus and Applied Analysis 19(3): 775–784.
  • [21] Kaczorek, T. (2016c). Positivity and stability of fractional descriptor time-varying discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 26(1): 5–13, DOI: 10.1515/amcs-2016-0001.
  • [22] Kaczorek, T. (2016d). Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems, International Journal of Applied Mathematics and Computer Science 26(2): 277–283, DOI: 10.1515/amcs-2016-0019.
  • [23] Kociszewski, R. (2013). Observer synthesis for linear discrete-time systems with different fractional orders, Pomiary Automatyka Robotyka 17(2): 376–381.
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  • [28] 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.
  • [29] Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
  • [30] Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Łódź University of Technology Publishing House, Łódź, (in Polish).
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  • [32] Sajewski, Ł (2016). Descriptor fractional discrete-time linear system with two different fractional orders and its solution, Bulletin of the Polish Academy of Sciences: Technical Sciences 64(1): 15–20.
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  • [35] Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429(10): 2640–2659.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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Bibliografia
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bwmeta1.element.baztech-df6b08f6-34c4-49ef-a16d-a9aaff093133
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