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

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 2, page 277-283
  • ISSN: 1641-876X

Abstract

top
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.

How to cite

top

Tadeusz Kaczorek. "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 (2016): 277-283. <http://eudml.org/doc/280112>.

@article{TadeuszKaczorek2016,
abstract = {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.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional system; descriptor system; nonlinear systems; reduced-order observer},
language = {eng},
number = {2},
pages = {277-283},
title = {Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems},
url = {http://eudml.org/doc/280112},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 2
SP - 277
EP - 283
AB - 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.
LA - eng
KW - fractional system; descriptor system; nonlinear systems; reduced-order observer
UR - http://eudml.org/doc/280112
ER -

References

top
  1. Cuihong, W. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197-206. Zbl1282.93228
  2. Dai, L. (1989). Singular Control Systems, Lecture Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin. Zbl0669.93034
  3. 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. Zbl0681.93036
  4. Gantmacher, F.R. (1960). The Theory of Matrices, Chelsea Publishing Co., New York, NY. Zbl0088.25103
  5. Guang-ren, D. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY. Zbl1227.93001
  6. Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press, J. Wiley, New York, NY. Zbl0784.93002
  7. 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. Zbl1171.93331
  8. 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. Zbl1235.34019
  9. Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292. Zbl1170.93016
  10. Kaczorek, T. (2001). Full-order perfect observers for continuous-time linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 49(4). Zbl1007.93008
  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. Zbl1221.93002
  13. Kaczorek, T. (2012a). Checking of the positivity of descriptor linear systems with singular pencils, Archive of Control Sciences 22(1): 77-86. Zbl1270.93057
  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. Zbl1286.93086
  16. Kaczorek, T. (2014a). Fractional descriptor observers for fractional descriptor continuous-time linear system, Archives of Control Sciences 24(1): 5-15. Zbl1301.93031
  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. Zbl1301.93031
  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. Zbl0661.93033
  21. Lewis, F.L. (1983). Descriptor systems, expanded descriptor equation and Markov parameters, IEEE Transactions on Automatic Control AC-28(5): 623-627. Zbl0517.93005
  22. Luenberger, D.G. (1977). Dynamical equations in descriptor form, IEEE Transactions on Automatic Control AC-22(3): 312-321. Zbl0354.93007
  23. Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14(5): 473-480. Zbl0398.93040
  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. Zbl1279.93027
  26. Oldham, K.B. and Spanier, J. (1974). The Fractional Calculus, Academic Press, New York, NY. Zbl0292.26011
  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. Zbl0924.34008
  29. Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27: 103-140. Zbl0416.65026
  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. Zbl1147.93033

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.