Singular fractional linear systems and electrical circuits

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 2, page 379-384
  • ISSN: 1641-876X

Abstract

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A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.

How to cite

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Tadeusz Kaczorek. "Singular fractional linear systems and electrical circuits." International Journal of Applied Mathematics and Computer Science 21.2 (2011): 379-384. <http://eudml.org/doc/208054>.

@article{TadeuszKaczorek2011,
abstract = {A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {singular; fractional system; linear circuit; regular pencil; supercapacitor; supercoil},
language = {eng},
number = {2},
pages = {379-384},
title = {Singular fractional linear systems and electrical circuits},
url = {http://eudml.org/doc/208054},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Singular fractional linear systems and electrical circuits
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 2
SP - 379
EP - 384
AB - A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils.
LA - eng
KW - singular; fractional system; linear circuit; regular pencil; supercapacitor; supercoil
UR - http://eudml.org/doc/208054
ER -

References

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  6. Kaczorek, T. (2004). Infinite eigenvalue assignment by outputfeedbacks for singular systems, International Journal of Applied Mathematics and Computer Science 14(1): 19-23. Zbl1171.93331
  7. Kaczorek, T. (2007a). Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London. Zbl1114.15019
  8. Kaczorek, T. (2007b). Realization problem for singular positive continuous-time systems with delays, Control and Cybernetics 36(1): 47-57. Zbl1293.93378
  9. 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
  10. Kaczorek, T. (2009). Selected Problems in the Theory of Fractional Systems, Białystok Technical University, Białystok, (in Polish). 
  11. 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
  12. Kaczorek, T. (2011). Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica 3(1), (in press). 
  13. Kucera, V. and Zagalak, P. (1988). Fundamental theorem of state feedback for singular systems, Automatica 24(5): 653-658. Zbl0661.93033
  14. Podlubny I. (1999). Fractional Differential Equations, Academic Press, New York, NY. Zbl0924.34008
  15. Van Dooren, P. (1979). The computation of Kronecker's canonical form of a singular pencil, Linear Algebra and Its Applications 27(1): 103-140. Zbl0416.65026

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