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Full-order observers for linear fractional multi-order difference systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is devoted to the construction of observers for linear fractional multi–order difference systems with Riemann–Liouville– and Grünwald–Letnikov–type operators. Basing on the Z-transform method the sufficient condition for the existence of the presented observers is established. The behaviour of the constructed observer is demonstrated in numerical examples.
Rocznik
Strony
891--989
Opis fizyczny
Bibliogr. 38 poz., wykr,
Twórcy
autor
  • Faculty of Computer Science Bialystok University of Technology Wiejska 45A, 15-351 Białystok, Poland, m.wyrwas@pb.edu.pl
Bibliografia
  • [1] L. Chen, W. Pan, R. Wu, and Y. He, “New result on finitetime stability of fractional-order nonlinear delayed systems”, Journal of Computational and Nonlinear Dynamics 10 (6), 5 pages (2015).
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  • [3] T. Kaczorek and P. Ostalczyk, “Responses comparison of the two discrete-time linear fractional state-space models”, Fractional Calculus and Applied Analysis 19 (4), 789–805, (2016).
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  • [5] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, 2011.
  • [6] D. Mozyrska, E. Girejko, and M. Wyrwas, “Fractional nonlinear systems with sequential operators”, Central European Journal of Physics 11 (10), 1295–1303 (2013).
  • [7] D. Mozyrska and E. Pawluszewicz, “Local controllability of nonlinear discrete-time fractional order systems”, Bull. Pol. Ac.: Tech. 61 (1), 251–256 (2013).
  • [8] D. Mozyrska, E. Pawłuszewicz, and M.Wyrwas, “Local observability and controllability of nonlinear discrete-time fractional order systems based on their linearisation”, International Journal of Systems Science 48 (4), 788–794, 2017.
  • [9] D. Mozyrska and M. Wyrwas, “Fractional discrete-time of Hegselmann-Krause’s type consensus model with numerical simulations”, Neurocomputing 216, 381–392 (2016).
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  • [14] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego-Boston-New York-London-Tokyo-Toronto, 1999.
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  • [16] T. Abdeljawad and F. M. Atıcı, “On the definitions of nabla fractional operators”, Abstract and Applied Analysis 2012, 13 pages (2012).
  • [17] F.M. Atıcı and P.W. Eloe, “Discrete fractional calculus with the nabla operator”, Electronic Journal of Qualitative Theory of Differential Equations Spec. Ed. I 2009 (3), 1–12 (2009).
  • [18] F. Chen, X. Luo, and Y. Zhou, “Existence results for nonlinear fractional difference equation”, Advances in Difference Equations 2011, 12 pages (2011).
  • [19] D. Mozyrska and E. Girejko, “Overview of the fractional h-difference operators”, In Frank-Olme Speck Alexandre Almeida, Luis Castro, editor, Operator Theory: Advances and Applications, volume 229, pages 253–267. Birkhäuser, 2013.
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  • [24] A. Dzieliński and D. Sierociuk, “Observer for discrete fractional order state-space systems”, 2nd IFAC Workshop on Fractional Diffrentation and its Applications, IFAC FDA ’06, Portugal, 2006, 524–529.
  • [25] D. Sierociuk, “Estimation and control of discrete-time dybnamical fractional systems described in state space”, Ph.D. thesis, Warsaw University of Technology, Warsaw 2007.
  • [26] M. Wyrwas and D. Mozyrska, Theoretical Developments and Applications of Non-Integer Order Systems, In Stefan Domek and Paweł Dworak, editors, Lecture Notes in Electrical Engineering, volume 357, chapter: “Stability of linear discrete– time systems with fractional positive orders”, 157–166, Springer, 2015.
  • [27] R.A.C. Ferreira and D.F.M. Torres, “Fractional h-difference equations arising from the calculus of variations”, Applicable Analysis and Discrete Mathematics 5 (1), 110–121 (2011).
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  • [29] F.M. Atıcı and P.W.Eloe, “A transform method in discrete fractional calculus”, International Journal of Difference Equations 2, 165–176 (2007).
  • [30] D. Mozyrska and M. Wyrwas, “The Z-transform method and delta type fractional difference operators”, Discrete Dynamics in Nature and Society 2015, 12 pages (2015).
  • [31] M. Busłowicz, “Robust stability of positive discrete–time linear systems of fractional order”, Bull. Pol. Ac.: Tech. 58 (4), 567–572 (2010).
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  • [33] M. Busłowicz and A. Ruszewski, “Necessary and sufficient conditions for stability of fractional discrete-time linear statespace systems”, Bull. Pol. Ac.: Tech. 61 (4), 779–786 (2013).
  • [34] D. Sierociuk and A. Dzieliński, “Stability of discrete fractional order state–space systems”, Journal of Vibration and Control 14 (9‒10), 1543–1556 (2008).
  • [35] R. Stanisławski and K.J. Latawiec, “Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: New necessary and sufficient conditions for the asymptotic stability”, Bull. Pol. Ac.: Tech. 61 (2), 353–361, (2013).
  • [36] R. Stanisławski and K.J. Latawiec, “Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems”, Bull. Pol. Ac.: Tech. 61 (2), 363–370, (2013).
  • [37] D. Mozyrska, “Multiparameter fractional difference linear control systems”, Discrete Dynamics in Nature and Society, 2014, 8 pages (2014).
  • [38] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Some applications of fractional order calculus”, Bull. Pol. Ac.: Tech. 58 (4), 583–592 (2010).
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-684b71e6-2c56-4722-9e31-b37bb40d9eb7
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