Perfect observers for fractional discrete-time linear systems
Kybernetika, Tome 52 (2016) no. 6, pp. 914-928
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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.
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.
DOI : 10.14736/kyb-2016-6-0914
Classification : 39A70, 93C05
Keywords: perfect observer; $h$-difference fractional operator; linear control system; singular system
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Pawluszewicz, Ewa. Perfect observers for fractional discrete-time linear systems. Kybernetika, Tome 52 (2016) no. 6, pp. 914-928. doi: 10.14736/kyb-2016-6-0914

[1] Abdeljawad, T., Baleanu, D.: Fractional differences and integration by parts. J. Comput. Analysis Appl. 13 (2011), 3, 574-582. | MR | Zbl

[2] Atici, F. M., Eloe, P. W.: A transform method in discrete fractional calculus. Int. J. Difference Equations 2 (2007), 165-176. | MR

[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. | DOI | Zbl

[4] Dai, L.: Observers for discrete singular systems. IEEE Trans. Automat. Control 33 (1988), 2, 187-191. | DOI | MR | Zbl

[5] Darouach, M., Boutat-Baddas, L.: Observers for a class of nonlinear singular systems. IEEE Trans. Automat. Control 53 (2008), 11, 2627-2633. | DOI | MR

[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. | DOI

[7] Dzielinski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci. Tech. Sci. 58 (2010), 4, 583-59. | DOI | Zbl

[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. | DOI | MR | Zbl

[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. | DOI

[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. | DOI

[11] Isidori, A.: Nonlinear Control Theory. Springer, 1991. | Zbl

[12] Kaczorek, T.: Full-order perfect observers for continuous-time linear systems. Pomiary, Automatyka, Kontrola 1 (2001), 3-6. | Zbl

[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. | DOI

[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

[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. | DOI | MR

[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. | DOI | MR

[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. | DOI | MR

[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. | DOI

[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. | DOI

[20] Slawinski, M., Kaczorek, T.: Perfect observers for continuous time linear systems. Pomiary, Automatyka, Kontrola 1 (2004), 39-44.

[21] Sontag, E. D.: Mathematical Control Theory. Springer 1998. | DOI | MR | Zbl

[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.

[23] Wolowich, W. A.: Linear Multivariable Systems. Springer-Verlag, 1974. | DOI | MR

[24] Wyrwas, M., Pawluszewicz, E., Girejko, E.: Stability of nonlinear $h$- difference systems with $n$ fractional orders. Kybernetika 51 (2015), 1, 112-136. | DOI | MR | Zbl

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