Descriptor fractional linear systems with regular pencils

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 2, page 309-315
  • ISSN: 1641-876X

Abstract

top
Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.

How to cite

top

Tadeusz Kaczorek. "Descriptor fractional linear systems with regular pencils." International Journal of Applied Mathematics and Computer Science 23.2 (2013): 309-315. <http://eudml.org/doc/257114>.

@article{TadeuszKaczorek2013,
abstract = {Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {descriptor system; fractional; system; regular pencil},
language = {eng},
number = {2},
pages = {309-315},
title = {Descriptor fractional linear systems with regular pencils},
url = {http://eudml.org/doc/257114},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Descriptor fractional linear systems with regular pencils
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 2
SP - 309
EP - 315
AB - Methods for finding solutions of the state equations of descriptor fractional discrete-time and continuous-time linear systems with regular pencils are proposed. The derivation of the solution formulas is based on the application of the Z transform, the Laplace transform and the convolution theorems. Procedures for computation of the transition matrices are proposed. The efficiency of the proposed methods is demonstrated on simple numerical examples.
LA - eng
KW - descriptor system; fractional; system; regular pencil
UR - http://eudml.org/doc/257114
ER -

References

top
  1. Dodig, M. and Stosic, M. (2009). Singular systems state feedbacks problems, Linear Algebra and Its Applications 431(8): 1267-1292. Zbl1170.93016
  2. Dai, L. (1989). Singular Control Systems, Lectures Notes in Control and Information Sciences, Vol. 118, Springer-Verlag, Berlin. Zbl0669.93034
  3. Fahmy, M.H and O'Reill, J. (1989). Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues 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. 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. 
  6. Kaczorek, T. (2011a). Positive linear systems consisting of n subsystems with different fractional orders, IEEE Transactions on Circuits and Systems 58(7): 1203-1210. 
  7. Kaczorek, T. (2011b). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin. Zbl1221.93002
  8. Kaczorek, T. (2010a). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458. Zbl1220.78074
  9. Kaczorek, T. (2010b). Practical stability and asymptotic stability of positive fractional 2D linear systems, Asian Journal of Control 12(2): 200-207. 
  10. Kaczorek, T. (2012a). Descriptor fractional linear systems with regular pencils, Asian Journal of Control 15(4): 1-14. 
  11. 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
  12. Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London. Zbl1114.15019
  13. Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57. Zbl1293.93378
  14. Kaczorek, T. (2004). Infinite eigenvalue assignment by an output feedbacks for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23. Zbl1171.93331
  15. Kaczorek, T. (1992). Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York, NY. Zbl0784.93002
  16. Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658. Zbl0661.93033
  17. Luenberger, D.G. (1978). Time-invariant descriptor systems, Automatica 14: 473-480. Zbl0398.93040
  18. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Zbl0924.34008
  19. Wang, C. (2012). New delay-dependent stability criteria for descriptor systems with interval time delay, Asian Journal of Control 14(1): 197-206. Zbl1282.93228
  20. 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
  21. Yan L., YangQuan C., Hyo-Sung A., (2011c). Fractional-order iterative learning control for fractional-order systems, Asian Journal of Control 13(1): 54-63. Zbl1248.93085

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.