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2016 | 26 | 2 | 277-283
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
26
Numer
2
Strony
277-283
Opis fizyczny
Daty
wydano
2016
otrzymano
2015-01-19
poprawiono
2015-03-10
zaakceptowano
2015-06-10
Twórcy
  • Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • Cuihong, W. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197-206.
  • Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin.
  • 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.
  • Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY.
  • Guang-ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.
  • Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, J. Wiley, New York, NY.
  • 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.
  • 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.
  • Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292.
  • Kaczorek, T. (2001). Full-order perfect observers for continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(4).
  • Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203-1210.
  • Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • Kaczorek, T. (2012a). Checking of the positivity of descriptor linear systems with singular pencils, Archive of Control Sciences 22(1): 77-86.
  • 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.
  • Kaczorek, T. (2013). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1051-1064.
  • Kaczorek, T. (2014a). Fractional descriptor observers for fractional descriptor continuous-time linear system, Archives of Control Sciences 24(1): 5-15.
  • 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.
  • 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.
  • Kociszewski, R. (2013). Observer synthesis for linear discrete-time systems with different fractional orders, Pomiary Automatyka Robotyka (2): 376-381, (on CD-ROM).
  • Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658.
  • Lewis, F.L. (1983). Descriptor systems, expanded descriptor equation and Markov parameters, IEEE Transactions on Automatic Control AC-28(5): 623-627.
  • Luenberger, D.G. (1977). Dynamical equations in descriptor form, IEEE Transactions on Automatic Control AC-22(3): 312-321.
  • Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14(5): 473-480.
  • Matignon, D. (1996). Stability result on fractional differential equations with applications to control processing, IMACSSMC Proceedings, Lille, France, pp. 963-968.
  • 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.
  • Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY.
  • Ostalczyk, P. (2008). Epitome of the Fractional Calculus: Theory and Its Applications in Automatics, Technical University of Łódź Press, Łódź, (in Polish).
  • Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY.
  • Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140.
  • 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.
  • Virnik, E. (2008). Stability analysis of positive descriptor systems, Linear Algebra and Its Applications 429: 2640-2659.
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Bibliografia
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