Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps.
Rocznik
Tom
Strony
251--256
Opis fizyczny
Bibliogr. 21 poz., rys., tab.
Twórcy
autor
autor
- Faculty of Computer Science, Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland
Bibliografia
- [1] M. Busłowicz, “Robust stability of positive discrete-time linear systems of fractional order”, Bull. Pol. Ac.: Tech. 58 (4), 567-572 (2010).
- [2] I. Podlubny, Fractional Differential Systems, Academic Press, San Diego, 1999.
- [3] D. Sierociuk and D. Dzieliński, “Fractional Kalman filter algorithm for the states parameters and order of fractional system estimation”, Int. J. Appl. Math. Comp. Sci. 16 (1), 129-140 (2006).
- [4] T. Abdeljawad, “On Riemann and Caputo fractional differences”, Comp. and Math. with Appl. 13 (3), 1602-1611 (2011).
- [5] F.M. Atici and P.W. Eloe, “Initial value problems in discrete fractional calculus”, Proc. American Mathematical Society S 0002-9939(08)09626, 3-9 (2009).
- [6] T. Kaczorek, Selected Problems of Fractional Systems Theory, Bialystok University of Technology, Białystok, 2009, (in Polish).
- [7] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integralsand Derivatives: Theory and Applications, Gordon and Breach Science Publishers S.A., Yverdon, 1993.
- [8] M. Busłowicz, “Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders”, Bull. Pol. Ac.: Tech. 60 (2), 279-284 (2012).
- [9] F. Chen, X. Luo, and Y. Zhou, “Existence results for nonlinear fractional difference equation”, Advances in Difference Eq. ID 713201, 1-12 (2011).
- [10] G.A. Anastassiou, Intelligent Mathematics: ComputationalAnalysis, Springer, Berlin, 2011.
- [11] T. Kaczorek, “Fractional positive linear systems”, Kybernetes 38 (7/8), 1059-1078 (2009).
- [12] T. Kaczorek, “Reachability of cone fractional continuous-time linear systems”, Int. J. Appl. Math. Comput. Sci. 19 (1), 89-93 (2009).
- [13] A. Ruszewski and N. Nartowicz, “Stabilization of inertial plant with time delay using fractional order controller”, Acta Mechanicaet Automatica 5 (2), 117-121 (2011).
- [14] J. Klamka, “Controllability of nonlinear discrete systems”, Int. J. Appl. Math. Comput. Sci. 12 (2), 173-180 (2002).
- [15] J. Klamka, “Local controllability of fractional discrete-time semilinear systems”, Acta Mechanica et Automatica 5 (2), 55-58 (2011).
- [16] I.M. Graves. “Some mapping theorems”, Duke Math. J. 17 (2), 111-114 (1950).
- [17] S. Walczak, “A note on the controllability of nonlinear systems”, Math. Systems Theory 17, 351-356 (1984).
- [18] M.T. Holm, The Theory of Discrete Fractional Calculus: Developmentand Application, University of Nebraska, Lincoln, 2011.
- [19] D. Mozyrska and E. Girejko, “Overview of the fractional h-difference operators”, in Advances in Harmonic Analysisand Operator Theory - the Stefan Samko Anniversary Volume. Operator Theory: Advances and Applications, vol. 229, Birkh¨auser, Basel, 2013.
- [20] M. Bettayeb and S. Djennoune, “A note on the controllability and the obseravbility of fractional dyanmical systems”, in Proc. 2nd IFAC Workshop on Fractional Differentiation andits Application 1, 19-21 (2006).
- [21] T. Kaczorek, “Reachability and controllability to zero of positive fractional discrete-time systems”, Machine Intelligence andRobotic Control 6 (4), 139-143 (2007).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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