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Title: Perfect observers for fractional discrete-time linear systems (English)
Author: Pawluszewicz, Ewa
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 52
Issue: 6
Year: 2016
Pages: 914-928
Summary lang: English
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Category: math
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Summary: A perfect (exact) fractional observer of discrete-time singular linear control system of fractional order is studied. Conditions for its existence are given. The obtained results are applied to the detectability problem of the class of systems under consideration. (English)
Keyword: perfect observer
Keyword: $h$-difference fractional operator
Keyword: linear control system
Keyword: singular system
MSC: 39A70
MSC: 93C05
idZBL: Zbl 06707380
idMR: MR3607854
DOI: 10.14736/kyb-2016-6-0914
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Date available: 2017-02-13T11:44:52Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/145997
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Reference: [1] Abdeljawad, T., Baleanu, D.: Fractional differences and integration by parts..J. Comput. Analysis Appl. 13 (2011), 3, 574-582. Zbl 1225.39008, MR 2752428
Reference: [2] Atici, F. M., Eloe, P. W.: A transform method in discrete fractional calculus..Int. J. Difference Equations 2 (2007), 165-176. MR 2493595
Reference: [3] Bastos, N. R. O., Ferreira, R. A. C., Torres, D. F. M.: Necessary optimality conditions for fractional difference problems of the calculus of variations..Discrete Contin. Dyn. Syst. 29 (2011), 2, 417-437. Zbl 1209.49020, 10.3934/dcds.2011.29.417
Reference: [4] Dai, L.: Observers for discrete singular systems..IEEE Trans. Automat. Control 33 (1988), 2, 187-191. Zbl 0633.93025, MR 0922795, 10.1109/9.387
Reference: [5] Darouach, M., Boutat-Baddas, L.: Observers for a class of nonlinear singular systems..IEEE Trans. Automat. Control 53 (2008), 11, 2627-2633. MR 2474831, 10.1109/tac.2008.2007868
Reference: [6] Duarte-Mermoud, M. A., Mira, M. J., Pelissier, I. S., Travieso-Torres, J. C.: Evaluation of a fractional order PI controller applied to induction moror speed control..In: Proc. 8th IEEE Int. Conf. on Control and Automation, Xiamen 2010, pp. 573-577. 10.1109/icca.2010.5524496
Reference: [7] Dzielinski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus..Bull. Pol. Acad. Sci. Tech. Sci. 58 (2010), 4, 583-59. Zbl 1220.80006, 10.2478/v10175-010-0059-6
Reference: [8] Ferreira, R. A. C., Torres, D. F. M.: Fractional h-difference equations arising from the calculus of variations..Appl. Anal. Discrete Math. 5 (2011), 1, 110-121. Zbl 1289.39007, MR 2809039, 10.2298/aadm110131002f
Reference: [9] Fiacchini, M., Millerioux, G.: Deat-beat functional observers for discrete-time LVP systems with unknown inputs..IEEE Trans. Automat. Control 58 (2013), 12, 3230-3235. 10.1109/tac.2013.2261712
Reference: [10] Girejko, E., Mozyrska, D., Wyrwas, M.: Advances in the theory and applications of non-integer order systems..In: Comparison of $h$-difference fractional operators (W. Mitkowski, J. Kacprzyk, and J. Baranowski, eds.), Springer 257 (2013), pp. 191-197. 10.1007/978-3-319-00933-9_17
Reference: [11] Isidori, A.: Nonlinear Control Theory..Springer, 1991. Zbl 0672.00015
Reference: [12] Kaczorek, T.: Full-order perfect observers for continuous-time linear systems..Pomiary, Automatyka, Kontrola 1 (2001), 3-6. Zbl 1007.93008
Reference: [13] Kaczorek, T.: Advances in Modelling and control of non-integer-order systems..In: Perfect Observers of Fractional Descriptor Continuous-Time Linear System (K. J. Latawiec, M. Lukaniszyn and R. Stanislawski, eds.), Lecture Notes in Electrical Engineering, Springer International Publishing 320 (2015), pp. 3-12. 10.1007/978-3-319-09900-2_1
Reference: [14] Miller, K. S., B, Ross: Fractional difference calculus..In: Proc. Int. Symp. on Univalent Functions, Fractional Calculus and their Applications, Nihon University, K\=oriyama 1988, pp. 139-152. MR 1199147
Reference: [15] Mozyrska, D., Girejko, E.: Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary..In: Overview of the fractional h-difference operators, Springer 229 (2013), pp. 253-267. MR 3060418, 10.1007/978-3-0348-0516-2_14
Reference: [16] Mozyrska, D., Pawluszewicz, E., Wyrwas, M.: Local observability and controllability of nonlinear discrete-time fractional order systems based on their linearization..Int. J. Syst. Sci. 48 (2017), 4, 788-794. MR 3566271, 10.1080/00207721.2016.1216197
Reference: [17] Mozyrska, D., Wyrwas, M.: The $\mathcal{Z}$-transform method and delta-type fractional difference operators..Discrete Dynamics in Nature and Society 2015, pp. 47-58. MR 3321587, 10.1007/978-3-319-09900-2_5
Reference: [18] Mozyrska, D., Wyrwas, M., Pawluszewicz, E.: Stabilization of linear multi-parameter fractional difference control systems..In: Proc. 20th Int. Conf. on Methods and Models in Automation and Robotics MMAR'2015, Miedzyzdroje 2915, pp. 315-319. 10.1109/mmar.2015.7283894
Reference: [19] N'Doye, I., Darouach, M., Zasadzinski, M., Radhy, N.-E.: Observers design for singular fractional-order system..In: Proc. 50th Int. Conf. on Decision and Control and European Control Conference CDC-ECC'2011, Orlando 2011, pp. 4017-4022. 10.1109/cdc.2011.6161336
Reference: [20] Slawinski, M., Kaczorek, T.: Perfect observers for continuous time linear systems..Pomiary, Automatyka, Kontrola 1 (2004), 39-44.
Reference: [21] Sontag, E. D.: Mathematical Control Theory..Springer 1998. Zbl 0945.93001, MR 1640001, 10.1007/978-1-4612-0577-7
Reference: [22] Trigeassou, J. C., Poinot, T., Lin, J., Oustaloup, A., Levron, F.: Modelling and identification of a non integer order system..In: Proc. European Control Conference ECC'1999, Karlsruhe 1999, pp. 2453-2458.
Reference: [23] Wolowich, W. A.: Linear Multivariable Systems..Springer-Verlag, 1974. MR 0359881, 10.1007/978-1-4612-6392-0
Reference: [24] Wyrwas, M., Pawluszewicz, E., Girejko, E.: Stability of nonlinear $h$- difference systems with $n$ fractional orders..Kybernetika 51 (2015), 1, 112-136. Zbl 1340.39029, MR 3333836, 10.14736/kyb-2015-1-0112
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