Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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
Tom
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
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).
- [2] J. Gabano and T. Poinot, “Fractional modelling and identification of thermal systems”, Signal Processing 91, 531–541 (2011).
- [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).
- [4] T. Kaczorek, “A new approach to the realization problem for fractional discrete-time linear systems”, Bull. Pol. Ac.: Tech. 64 (1), 9–14, 2016.
- [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).
- [10] P. Ostalczyk, Discrete Fractional Calculus: Applications in Control and Image Processing, Series in Computer Vision – Volume 4, World Scientific Publishing Co, Singapore, 2016.
- [11] D. Sierociuk, T. Skovranek, M. Macias, I. Podlubny, I. Petras, A. Dzielinski, and P. Ziubinski, “Diffusion process modeling by using fractional-order models”, Applied Mathematics and Computation 257, 2–11 (2015)
- [12] R. Stanisławski, M. Rydel, and K.J. Latawiec, “Modeling of discrete-time fractional-order state space systems using the balanced truncation method”, Journal of the Franklin Institute 354(7), 3008‒3020, (2017).
- [13] A.A. Kilbas, H. M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North–Holland Mathematics Studies, 204. Elsevier Science B. V., Amsterdam, 2006.
- [14] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego-Boston-New York-London-Tokyo-Toronto, 1999.
- [15] K.S. Miller and B. Ross, “Fractional difference calculus”, In Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and their Applications, pages 139–152, Kōriyama, Japan, 1988. Nihon University.
- [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.
- [20] M.D. Ortigueira, F.J.V. Coito, and J.J. Trujillo, “Discretetime differential systems”, Signal Processing 107, 198–217 (2015).
- [21] S.R. Anderson and V. Kadirkamanathan, “Modelling and identification of nonlinear deterministic systems in deltadomain”, Automatica 43, 1859–1868 (2007).
- [22] M. Boutayeb, M. Darouach, and H. Rafaralahy, “Generalized state-space observers for chaotic synchronization and secure communication”, IEEE Transactions on Circuits and Systems, I: Fundamental Theory and Applications 49 (3), 345–349 (2002).
- [23] M. Darouach, M. Zasadzinski, and S. Xu, “Full-order observers for linear systems with unknown inputs”, IEEE Transactions on Automatic Control 39 (3), 606–609 (1994).
- [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).
- [28] N.R.O. Bastos, R.A.C. Ferreira, and D.F.M. Torres, “Discrete-time fractional variational problems”, Signal Processing 91 (3), 513–524 (2011).
- [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).
- [32] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete–time linear systems”, International Journal of Applied Mathematics and Computer Science 19 (2), 236–269 (2009).
- [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