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

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/bpasts.2019.130891

• Języki publikacji: EN

Abstrakty

EN

The Drazin inverse of matrices is applied to analysis of the pointwise completeness and of the pointwise degeneracy of the fractional descriptor linear discrete-time systems. Necessary and sufficient conditions for the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear discrete-time systems are established. It is shown that every fractional descriptor linear discrete-time systems is not pointwise complete and it is pointwise degenerated in one step (for i= 1).

Słowa kluczowe

EN

fractional; descriptor; pointwise completeness; pointwise degeneracy

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 6
• Strony: 989--993
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok

Bibliografia

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• [4] 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).
• [5] 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).
• [6] T. Kaczorek, “Drazin inverse matrix method for fractional descriptor discrete-time linear systems”, Bull. Pol. Ac.: Tech. 64(2), 1‒5 (2016).
• [7] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive hydrid linear systems described by the general model”, Archives of Control Sciences 2, 121‒131 (2010).
• [8] T. Kaczorek, “Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks”, Journal of Automation, Mobile Robotics and Ingelligent Systems4(1), 3‒7 (2010).
• [9] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
• [10] 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).
• [11] T. Kaczorek, K. Rogowski, Fractional Linear Systems and Electrical Circuits, Springer 2015.
• [12] T. Kaczorek and A. Ruszewski, “Application of the Drazin inverse of matrices to the pointwise completeness and the pointwise degeneracy of the fractional descriptor linear continuous-time systems”.
• [13] W. Malesza and D. Sierociuk, “Fractional variable order anti-windup control strategy”, Bull. Pol. Ac.: Tech. 66(4), 427‒432 (2018).
• [14] 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).
• [15] A. Olbrot, “On degeneracy and related problems for linear constant time-lag systems”, Ricerche di Automatica 3(3), 203‒220 (1972).
• [16] M.D. Ortigueira and J.T.M. Machado, “On fractional vectorial calculus”, Bull. Pol. Ac.: Tech. 66(4), 389‒402 (2018).
• [17] V.M. Popov, “Pointwise degeneracy of linear time-invariant delay-differential equations”, Journal of Differential Equation11, 541‒561 (1972).
• [18] W. Trzasko, M. Busłowicz, and T. Kaczorek, “Pointwise completeness of discrete-time cone-systems with delays”, Int. Proc. EUROCON, Warsaw, pp. 606‒611 (2007).

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).