Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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.
Rocznik
Tom
Strony
245--251
Opis fizyczny
Bibliogr. 35 poz.
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.
- [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, Springer, Berlin.
- [4] Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
- [5] Fahmy, M.M. and O’Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment, International Journal of Control 49(4): 1421–1431.
- [6] Gantmacher, F.R. (1959). The Theory of Matrices, Chelsea, London.
- [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.
- [24] Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653–658.
- [25] Lewis, F.L. (1983). Descriptor systems, expanded descriptor equation and Markov parameters, IEEE Transactions on Automatic Control 28(5): 623–627.
- [26] Luenberger, D.G. (1977). Dynamical equations in descriptor form, IEEE Transactions on Automatic Control 22(3): 312–321.
- [27] Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14(5): 473–480.
- [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).
- [31] Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
- [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.
- [33] Van Dooren, P. (1979). The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103–140.
- [34] Vinagre, B.M., Monje, C.A. and Calderon, A.J. (2002). Fractional order systems and fractional order control actions, IEEE Conference on Decision and Control, Las Vegas, NV, USA, pp. 2550–2554.
- [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).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-df6b08f6-34c4-49ef-a16d-a9aaff093133