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Characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of calculation of the characteristic equations of the standard and descriptor linear electrical circuits of integer and fractional orders is addressed. It is shown that the characteristic equations of standard and descriptor linear electrical circuits are independent of the method used in their analysis: the state space method, the mesh method and the node method. The considerations are illustrated by examples of standard and fractional linear electrical circuits.
Rocznik
Strony
209--216
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
autor
  • Faculty of Electrical Engineering, Białystok University of Technology, Wiejska 45D, 15-351 Białystok
Bibliografia
  • 1. Antsaklis P.J., Michel A.N. (2006), Linear Systems, Birkhauser, Boston.
  • 2. Cholewicki T. (1967), Theoretical Electrotechnics, WNT, Warszawa (in Polish).
  • 3. Dzieliński A., Sierociuk D., Sarwas G. (2009), Ultracapacitor parameters identification based on fractional order model, Proc. ECC’09, Budapest.
  • 4. Farina L., Rinaldi S. (2000), Positive Linear Systems; Theory and Applications, J. Wiley, New York.
  • 5. Kaczorek T. (1992), Linear Control Systems vol. 1, Research Studies Press, J. Wiley, New York.
  • 6. Kaczorek T. (2002), Positive 1D and 2D Systems, Springer-Verlag, London.
  • 7. Kaczorek T. (2008a), Fractional positive continuous-time systems and their reachability, Int. J. Appl. Math. Comput. Sci., 18(2), 223–228.
  • 8. Kaczorek T. (2008b), Practical stability of positive fractional discretetime linear systems, Bull. Pol. Acad. Sci. Tech., 56(4), 313–317.
  • 9. Kaczorek T. (2009), Asymptotic stability of positive fractional 2D linear systems, Bull. Pol. Acad. Sci. Tech., 57(3), 289–292.
  • 10. Kaczorek T. (2010), Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Techn., 58(3), 453–458.
  • 11. Kaczorek T. (2011a), Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, 58(6), 1203–1210.
  • 12. Kaczorek T. (2011b), Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, 5(2), 42–51.
  • 13. Kaczorek T. (2011c), Positive electrical circuits and their reachability, Archives of Electrical Engineering, 60(3), 283–301.
  • 14. Kaczorek T. (2011d), Controllability and observability of linear electrical circuits, Electrical Review, 87(9a), 248–254.
  • 15. Kaczorek T. (2012a), Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • 16. Kaczorek T. (2012b), Positive unstable electrical circuits, Electrical Review, 88(5a), 187–192.
  • 17. Kaczorek T. (2013a), Positive fractional linear electrical circuits. Proceedings of SPIE, 8903, Bellingham WA, USA, Art. No 3903–35.
  • 18. Kaczorek T. (2013b), Constructability and observability of standard and positive electrical circuits, Electrical Review, 89(7), 132–136.
  • 19. Kaczorek T. (2013c), Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review, 89(10), 200–203.
  • 20. Kaczorek T. (2014a), Polynomial approach to fractional descriptor electrical circuits, Computational Models for Business and Engineering Domains - ITHEA, Rzeszow, Poland.
  • 21. Kaczorek T. (2014b), Decoupling zeros of positive continuous-time linear systems and electrical circuit, Advances in Systems Science. Advances in Intelligent Systems and Computing, 240, 1–15.
  • 22. Kaczorek T. (2015a), A class of positive and stable time-varying electrical circuits, Electrical Review, 91(5), 121–124.
  • 23. Kaczorek T. (2015b), Normal positive electrical circuits, IET Circuits Theory and Applications, 9(5), 691–699.
  • 24. Kaczorek T. (2016), Minimal-phase positive electrical circuits, Electrical Review, 92(3), 182–189.
  • 25. Kaczorek T., Rogowski K. (2015), Fractional Linear Systems and Electrical Circuits, Studies in Systems, 13, Springer International Publishing.
  • 26. Kailath T. (1980), Linear Systems, Prentice-Hall, Englewood Cliffs, New York.
  • 27. Oldham K.B., Spanier J. (1974), The Fractional Calculus, Academic Press, New York.
  • 28. Ostalczyk P. (2008), Epitome of the fractional calculus: Theory and its Applications in Automatics, Technical University of Łódź Press, Łódź (in Polish).
  • 29. Ostalczyk P. (2016) Discrete Fractional Calculus: Selected Applications in Control and Image Processing, Series in Computer Vision, 4.
  • 30. Podlubny I. (1999), Fractional Differential Equations, Academic Press, San Diego.
  • 31. Rosenbrock H. (1970), State-Space and Multivariable Theory, J. Wiley, New York.
  • 32. Sajewski Ł. (2016), Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders, Multidimensional Systems and Signal Processing, 27(1), 27–41.
  • 33. Vinagre B.M., Monje C.A., Calderon A.J. (2002), Fractional order systems and fractional order control actions, Lecture 3 IEEE CDC’02 TW#2: Fractional calculus Applications in Automatic Control and Robotics.
  • 34. Wolovich W.A. (1974), Linear Multivariable Systems, SpringerVerlag, New York.
  • 35. Żak S.H. (2003), Systems and Control, Oxford University Press, New York.
Uwagi
This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8800c4e2-562c-4ebe-a821-e2f69f271a14
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