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Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 29-33
  • ISSN: 1641-876X

Abstract

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The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.

How to cite

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Tadeusz Kaczorek. "Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 29-33. <http://eudml.org/doc/275899>.

@article{TadeuszKaczorek2013,
abstract = {The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Drazin inverse; descriptor; fractional system; discrete-time system; linear system},
language = {eng},
number = {1},
pages = {29-33},
title = {Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils},
url = {http://eudml.org/doc/275899},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 29
EP - 33
AB - The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
LA - eng
KW - Drazin inverse; descriptor; fractional system; discrete-time system; linear system
UR - http://eudml.org/doc/275899
ER -

References

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  2. Bru, R., Coll, C. and Sanchez, E. (2000). About positively discrete-time singular systems, in N.E. Mastorakis (Ed.) System and Control: Theory and Applications, Electrical and Computer Engineering Series, World Scientific and Engineering Society, Athens, pp. 44-48. 
  3. Bru, R., Coll, C. and Sanchez, E. (2002). Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra and Applications 349(1-3): 1-10. Zbl1006.93006
  4. Campbell, S.L., Meyer, C.D. and Rose, N.J. (1976). Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM Journal on Applied Mathematics 31(3): 411-425. Zbl0341.34001
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  8. 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
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  12. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
  13. 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
  14. Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London. Zbl1114.15019
  15. Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57. Zbl1293.93378
  16. Kaczorek, T. (2010). Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(3): 453-458. Zbl1220.78074
  17. Kaczorek, T. (2011a). Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archives of Control Sciences 21(3): 287-298. Zbl1264.93096
  18. Kaczorek, T. (2011b). Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin. Zbl1221.93002
  19. Kaczorek T. (2011c). Singular fractional discrete-time linear systems, Control and Cybernetics 40(3): 1-8. Zbl1318.93058
  20. Kaczorek T. (2011d). Reduction and decomposition of singular fractional discrete-time linear systems, Acta Mechanica et Automatica 5(4): 1-5. Zbl1318.93058
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