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The pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems

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Abstrakty
EN
Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional order systems are established. It is shown that if the fractional system is pointwise complete in one step (q = 1), then it is also pointwise complete for q = 2, 3…
Twórcy
autor
  • Bialystok University of Technology, Faculty of of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok, Poland
autor
  • Bialystok University of Technology, Faculty of of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] A.K. Choundhury, “Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems”, Int. J. Control 16 (6), 1083–1100 (1972).
  • [2] A. Olbrot, “On degeneracy and related problems for linear constant time-lag systems”, Ricerche di Automatica 3 (3), 203–220 (1972).
  • [3] V.M. Popov, “Pointwise degeneracy of linear time-invariant delay-differential equations”, J. Differ. Equ. 11, 541–561 (1972).
  • [4] M. Busłowicz, R. Kociszewski, and W. Trzasko, “Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays”, Zeszyty Naukowe Pol. Śląskiej, Automatyka 151, 55–56 (2008).
  • [5] W. Trzasko, M. Busłowicz, and T. Kaczorek, “Pointwise completeness of discrete-time cone-systems with delays”, Int. Proc. EUROCON, Warsaw, 606–611 (2007).
  • [6] M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order”, Zeszyty Naukowe Pol. Śląskiej, Automatyka 151, 19–24 (2008).
  • [7] T. Kaczorek, “The pointwise completeness and the pointwise degeneracy of fractional descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech. 67 (6), 989–993 (2019). doi: 0.24425/bpasts.2019.130891.
  • [8] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
  • [9] T. Kaczorek and M. Busłowicz, “Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems”, Journal of Automation, Mobile Robotics and Intelligent Systems 3 (1), 8–11 (2009).
  • [10] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive hydrid linear systems described by the general model”, Arch. Control Sci. 20 (2), 121–131 (2010).
  • [11] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks”, Journal of Automation, Mobile Robotics and Ingelligent Systems 4 (1), 3–7 (2010).
  • [12] E. Girejko, D. Mozyrska, and M. Wyrwas, “Behaviour of fractional discrete-time consensus models with delays for summator dynamics”, Bull. Pol. Ac.: Tech. 66 (4), 403–410 (2018).
  • [13] T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits, Springer, Cham 2015.
  • [14] W. Malesza and D. Sierociuk, “Fractional variable order antiwindup control strategy”, Bull. Pol. Ac.: Tech. 66 (4), 427–432 (2018).
  • [15] D. Mozyrska, P. Ostalczyk and M. Wyrwas, “Stability conditions for fractional-order linear equations with delays”, Bull. Pol. Ac.: Tech. 66 (4), 449–454 (2018).
  • [16] M.D. Ortigueira and J.T.M. Machado, “On fractional vectorial calculus”, Bull. Pol. Ac.: Tech. 66 (4), 389–402 (2018).
  • [17] Ł. Sajewski, “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller”, Bull. Pol. Ac.: Tech. 65 (5), 709–714 (2017).
  • [18] T. Kaczorek, “Application of the Drazin inverse of matrices to analysis of the pointwise completeness and the pointwise degeneracy of the descriptor linear systems”, 15th International Conference Dynamical Systems Theory and Applications, December 2–5, 2019, Łódź, Poland (2019).
  • [19] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech. 64 (2), 1–5 (2016).
  • [20] T. Kaczorek and A. Ruszewski, “Application of the Drazin inverse of matrices to the pointwise completeness and the point-wise degeneracy of the fractional descriptor linear continuous-time systems”, Int. J. Appl. Math. Comput. Sci. 30 (2), 219–223 (2020).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
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Bibliografia
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