Application of the Drazin inverse to the analysis of pointwise completeness and pointwise degeneracy of descriptor fractional linear continuous-time systems

• Autorzy: Kaczorek Tadeusz , Ruszewski Andrzej

Identyfikatory

DOI

10.34768/amcs-2020-0017

• Języki publikacji: EN

Abstrakty

EN

The Drazin inverse of matrices is applied to the analysis of pointwise completeness and pointwise degeneracy of fractional descriptor linear continuous-time systems. It is shown that (i) descriptor linear continuous-time systems are pointwise complete if and only if the initial and final states belong to the same subspace, and (ii) fractional descriptor linear continuous-time systems are not pointwise degenerated in any nonzero direction for all nonzero initial conditions. The discussion is illustrated with examples of descriptor linear electrical circuits.

Słowa kluczowe

EN

pointwise completeness; pointwise degeneracy; fractional system; descriptor system

PL

zupełność punktowa; degeneracja punktowa; system ułamkowy; system deskryptorowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 2
• Strony: 219--223
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Kaczorek Tadeusz

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

autor

Ruszewski Andrzej

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

Bibliografia

• [1] Busłowicz, M. (2008). Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order, Scientific Journal of the Silesian University of Technology: Automation 151(1797): 19–24, (in Polish).
• [2] Busłowicz, M., Kociszewski, R. and Trzasko, W. (2006). Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays, Scientific Journal of the Silesian University of Technology: Automation 145(1728): 51–56, (in Polish).
• [3] Choundhury, A.K. (1972). Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems, International Journal of Control 16(6): 1083–1100.
• [4] Kaczorek, T. (2010a). Pointwise completeness and pointwise degeneracy of standard and positive hybrid linear systems described by the general model, Archives of Control Sciences 2(2): 121–131.
• [5] Kaczorek, T. (2010b). Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks, Journal of Automation, Mobile Robotics and Intelligent Systems 4(1): 3–7.
• [6] Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin.
• [7] Kaczorek, T. (2019). 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 on Dynamical Systems Theory and Applications, Łódź, Poland, pp. 198–204.
• [8] Kaczorek, T. and Busłowicz, M. (2009). Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems, Journal of Automation, Mobile Robotics and Intelligent Systems 3(1): 8–11.
• [9] Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.
• [10] Olbrot, A. (1972). On degeneracy and related problems for linear constant time-lag systems, Ricerche di Automatica 3(3): 203–220.
• [11] Popov, V.M. (1972). Pointwise degeneracy of linear time-invariant delay-differential equations, Journal of Differential Equations 11(3): 541–561.
• [12] Trzasko, W., Busłowicz, M. and Kaczorek T. (2007). Pointwise completeness of discrete-time cone-systems with delays, Proceedings of the International Conference on Computer as a Tool, EUROCON 2007, Warsaw, Poland, pp. 606–611.

Uwagi

PL

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