Controllability of linear convex combination of linear discrete-time fractional systems

• Autorzy: Kaczorek Tadeusz , Klamka Jerzy , Dzieliński Andrzej

Identyfikatory

DOI

10.24425/bpasts.2022.143102

• Języki publikacji: EN

Abstrakty

EN

In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.

Słowa kluczowe

EN

fractional order systems; controllability; linear convex combination

PL

system ułamkowego rzędu; sterowność; kombinacja wypukła liniowa

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2022
• Tom: Vol. 70, nr 5
• Strony: art. no. e143102
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kaczorek Tadeusz

• Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, Bialystok, Poland

• https://orcid.org/0000-0002-1270-3948

autor

Klamka Jerzy

• Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, Gliwice, Poland

• https://orcid.org/0000-0003-1574-9826

autor

Dzieliński Andrzej

• Warsaw University of Technology, Faculty of Electrical Engineering, ul. Koszykowa 75, Warsaw, Poland

• https://orcid.org/0000-0001-6963-8545

Bibliografia

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• [2] T. Crowder, “Linearization of quantum channels,” J. Geom. Phys., vol. 92, no. 6, pp. 157–166, 2015.
• [3] J. Klamka, Controllability of Dynamical Systems, ser. Studies in Systems, Decision and Control. Kluwer Academic Publishers. Dordrecht. The Netherlands, 1991, vol. 162.
• [4] J. Klamka, “Controllability of dynamical systems – a survey,” Arch. Control Sci., vol. 2, no. 3-4, pp. 281–307, 1993.
• [5] J. Klamka, “Controllability of dynamical systems. A survey,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 61, no. 2, pp. 335–342, 2013.
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• [7] J. Klamka, Controllability and Minimum Energy Control. Springer Verlag, Berlin, 2018.
• [8] A. Dzieliński and D. Sierociuk, “Reachability, controllability and observability of the fractional order discrete state-space system.” in Proceedings of the IEEE/IFAC International Conference on Methods and Models in Automation and Robotics, MMAR, 2007, pp. 129–134.
• [9] J. Klamka, A. Babiarz, and M. Niezabitowski, “Banach fixed-point theorem in semilinear controllability problems – a survey,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 64, no. 1, pp. 21–35, 2016.
• [10] T. Kaczorek and J. Klamka, “Convex linear combination of the controllability pairs for linear systems,” Control Cybern., vol. 50, no. 1, pp. 1–11, 2021.
• [11] T. Kaczorek, Selected Problems of Fractional Systems Theory. Springer, Berlin, Heidelberg, 2011.
• [12] F. Gantmacher, The Theory of Matrices. Chelsea Publ. Comp., London, 1959.
• [13] T. Kaczorek, “Positive and stable electrical circuits with state feedbacks,” Arch. Electr. Eng., vol. 67, no. 3, pp. 563–578, 2018.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).