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A new extension of the Cayley-Hamilton theorem to fractional different orders linear systems

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Języki publikacji
EN
Abstrakty
EN
The classical Cayley–Hamilton theorem is extended to fractional different order linear systems. The new theorems are applied to different orders fractional linear electrical circuits. The applications of new theorems are illustrated by numerical examples.
Rocznik
Strony
art. no. e139960
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
  • Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] F.R. Chang and C.M. Chan, “The generalized Cayley–Hamilton theorem for standard pencils”, Syst. Control Lett., vol. 18, no. 3, pp. 179–182, 1992.
  • [2] F.R. Gantmacher, The Theory of Matrices, London: Chelsea Pub. Comp., 1959.
  • [3] T. Kaczorek, “An extension of the Cayley–Hamilton theorem to different orders fractional linear systems and its application to electrical circuits”, IEEE Trans. Circuits Syst. II-Express Briefs, vol. 66, no. 7, pp. 1169–1171, July 2019, doi: 10.1109/TCSII.2018.2873176.
  • [4] T. Kaczorek, “An extension of the Cayley–Hamilton theorem for non-square block matrices and computation of the left and right inverses of matrices”, Bull. Pol. Acad. Sci. Techn., vol. 43, no. 1, pp. 49–56, 1995.
  • [5] T. Kaczorek, “An extension of the Cayley–Hamilton theorem for singular 2D linear systems with non-square matrices”, Bull. Pol. Acad. Sci. Tech. Sci., vol. 43, no. 1, pp. 39–48, 1995.
  • [6] T. Kaczorek, “Generalizations of Cayley–Hamilton theorem for n-D polynomial matrices”, IEEE Trans. Autom. Contr., vol. 50, no. 5, pp. 671–674, 2005.
  • [7] T. Kaczorek, Linear Control Systems, vol. I, II, New York: Re-search Studies Press, J. Wiley, 1992–1993.
  • [8] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin 2011.
  • [9] P. Lancaster, Theory of Matrices, New York: Acad. Press, 1969.
  • [10] F.L. Lewis, “Cayley–Hamilton theorem and Fadeev’s method for the matrix pencil [sE-A]”, in Proc. 22nd IEEE Conf. Decision Control, 1982, pp. 1282–1288.
  • [11] F.L. Lewis, “Further remarks on the Cayley–Hamilton theorem and Fadeev’s method for the matrix pencil [sE-A]”, IEEE Trans. Automat. Control, vol. 31, no. 7, pp. 869–870, 1986.
  • [12] B.G. Mertizios and M.A. Christodoulous, “On the generalized Cayley–Hamilton theorem”, IEEE Trans. Autom. Control, vol. 31 no. 1, pp. 156–157, 1986.
  • [13] N.M. Smart and S. Barnett, “The algebra of matrices in n-dimensional systems”, IMA J. Math. Control Inform., vol. 6, pp. 121–133, 1989.
  • [14] N.J. Theodoru, “M-dimensional Cayley–Hamilton theorem”, IEEE Trans. Autom. Control, vol. AC-34, no. 5, 563–565, 1989.
  • [15] J. Victoria, “A block Cayley–Hamilton theorem”, Bull. Math. Soc. Sci. Math. Roum., vol. 26, no. 1, pp. 9397, 1982.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-10d8c394-9b46-430a-a1ca-381c0d6c8b57
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