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Shuffle algorithm for fractional descriptor Roesser type continuous-time linear systems

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Warianty tytułu
PL
Algorytm przesuwania dla liniowych układów deskryptorowych niecałkowitego rzędu ciągłych typu Roessera
Języki publikacji
EN
Abstrakty
EN
The shuffle algorithm is applied to analysis of the fractional descriptor Roesser type continuous-time linear systems. Using the shuffle algorithm the fractional descriptor linear system is reduced to the equivalent standard system and the system is decomposed into dynamic and static parts. Procedure for computation of the matrices of equivalent standard system and of the dynamical and static parts of the system is proposed.
PL
Algorytm przesuwania jest stosowany do analizy ułamkowych deskryptorowych układów liniowych ciągłych typu Roesser. Stosując algorytm przesuwania, liniowy układ deskryptorowy niecałkowitego rzędu jest redukowany do równoważnego układu standardowego, oraz jest rozkładany na część dynamiczną i statyczną. Zaproponowano procedurę obliczania macierzy równoważnego układu standardowego oraz metodę obliczania części dynamicznej i statycznej.
Twórcy
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
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  • [2] Busłowicz M. (2012) “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Acad. Sci. Tech., vol. 60, no. 2, 279-284.
  • [3] Busłowicz M. and Kaczorek T. (2009) “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, 263- 169.
  • [4] Bru R, Coll C, Romero-Vivo S, Sanchez E. (2003) Some problems about structural properties of positive descriptor systems, Positive systems (Rome, 2003), Lecture Notes in Control and Inform. Sci., 294, Springer, Berlin, 233-240.
  • [5] Bru R, Coll C, Sanchez E. (2000) “About positively discrete-time singular systems, System and Control: theory and applications”, Electr. Comput. Eng. Ser., World Sci. Eng. Soc. Press, Athens, 44- 48.
  • [6] Bru R, Coll C, Sanchez E. (2002) “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl; 349, 1-10.
  • [7] Dai L. (1989) Singular control systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin.
  • [8] Dodig M, Stosic M. (2009) “Singular systems state feedbacks problems”, Linear Algebra and its Applications, 431 (8), 1267- 1292.
  • [9] Farina L. and Rinaldi S. (2000) Positive Linear Systems; Theory and Applications, J. Wiley, New York.
  • [10] Guang-Ren Duan (2010) Analysis and Design of Descriptor Linear Systems, Springer, New York.
  • [11] Kaczorek T. (2021) “Application of the shuffle algorithm to analysis of the fractional descriptor continuous-time linear systems”, Proc. Of MMAR Conf. Miedzyzdroje.
  • [12] Kaczorek T. (2011) “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences, vol. 21, no. 3, 287-298.
  • [13] Kaczorek T. (2004) “Infinite eigenvalue assignment by output feedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci., vol. 14, no. 1, 19-23.
  • [14] Kaczorek T. (2002) Positive 1D and 2D Systems, Springer-Verlag, London.
  • [15] Kaczorek T. (1992) Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York.
  • [16] Kaczorek T. (2013) “Application of Drazin inverse to analysis of descriptor fractional discrete-time linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci., vol. 23, no. 1, 29-34.
  • [17] Kaczorek T. (2010) “Positive linear systems with different fractional orders”, Bull. Pol. Acad. Sci. Tech., vol. 58, no. 3, 453- 458.
  • [18] Kaczorek T. (2011) Selected Problems of Fractional System Theory, Springer-Verlag, Berlin.
  • [19] Kaczorek T. (2011) “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, 1203-1210.
  • [20] Kaczorek T. (2012) “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac. Sci. Tech., vol. 60, no. 1, 9-12.
  • [21] Kaczorek T. and Borawski K. (2016) “Fractional descriptor continuous-time linear systems described by the Caputo Fabrizio derivative”, Int.J. Appl. Math. Comput. Sci. vol. 3, no.3, 533-541.
  • [22] Kaczorek T. and Rogowski K. (2014) Fractional Linear Systems and Electrical Circuits, Springer Cham Springer.
  • [23] Kucera V. and Zagalak P. (1988) “Fundamental theorem of state feedback for singular systems”, Automatica, vol. 24, no. 5, 653- 658.
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  • [25] Luenberger D.G. (1978) “Time-invariant descriptor systems”, Automatica, vol. 14, 473-480.
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  • [27] Podlubny I. (1999) Fractional Differential Equations, Academic Press, San Diego.
  • [28] Rogowski K. (2020) “General response formula for CFD fractional 2D continuous linear systems described by the Roesser model”, Symmetry, vol. 12 no. 12, 1934.
  • [29] Ruszewski A. (2019) “Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems”, Bull. Pol. Acad. Sci. Techn., vol. 67, no. 3, 509-515.
  • [30] Sajewski Ł. (2017) “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller”, Bull. Pol. Acad. Sci. Techn., vol. 65, no. 5, 709-714.
  • [31] Virnik E. (2008) “Stability analysis of positive descriptor systems”, Linear Algebra and its Applications, vol. 429, 2640- 2659.
  • [32] Xiang-Jun W., Zheng-Mao W. and Jun-Guo L. (2008) “Stability analysis of a class of nonlinear fractional-order systems”, IEEE Trans. Circuits and Systems-II, Express, Vol. 55, no. 11, 1178— 1182.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
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Bibliografia
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