The Floquet-Lyapunov transformation for fractional discrete-time linear systems with periodic parameters

• Autorzy: Kaczorek Tadeusz , Ruszewski Andrzej

Identyfikatory

DOI

10.24425/acs.2024.149653

• Języki publikacji: EN

Abstrakty

EN

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.

Słowa kluczowe

EN

Floquet-Lyapunov transformation; fractional; discrete-time; linear; periodic parameters

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2024
• Tom: Vol. 34, No. 1
• Strony: 83--89
• Opis fizyczny: Bibliogr. 12 poz., wzory

Twórcy

autor

Kaczorek Tadeusz

• Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland

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

autor

Ruszewski Andrzej

• Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland

• https://orcid.org/0000-0003-0095-6486

Bibliografia

• [1] P.J. Antsaklis and A.N. Michel: Linear Systems, Birkhauser, Boston, 1997.
• [2] J.J. DaCunha and J.M. Davis: A unified Floquet theory for discrete, continuous and hybrid periodic linear systems. Journal of Differential Equations, 251(11), (2011), 2987-3027. DOI: 10.1016/j.jde.2011.07.023
• [3] G. Floquet: Sur les équations différentielles linéaires à coefficients périodiques. Annales scientifiques de l’École Normale Supérieure, Ser. 2, 12 (1883), 47-88.
• [4] F.G. Gantmacher: The Theory of Matrices. Chelsea, New York, 1959.
• [5] T. Kaczorek: Floquet-Lyapunov transformation for regular 2-D linear systems. Bulletin of the Polish Academy of Sciences. Technical Sciences, 39 (1991), 673-679.
• [6] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer, Berlin, 2011.
• [7] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits. Springer, Cham, 2015.
• [8] W. Mitkowski: Outline of Control Theory. AGH Publisher, Kraków, 2019, ( in Polish).
• [9] P. Ostalczyk: Discrete Fractional Calculus. World Scientific, River Edgle NJ, 2016.
• [10] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
• [11] T.J. Osler: Leibniz rule for fractional derivatives generalized and application to infinite. SIAM Journal on Applied Mathematics, 18(3), (1970), 658-674. DOI: 10.1137/0118059
• [12] J. Sreedhar and P. Van Dooren: Discrete-time Periodic Systems: A Floquet Approach. In Proceedings of the Conference on Information Sciences and Systems, Baltimore, (1993), 194-195.

Uwagi

This work was supported by National Science Centre in Poland under work No. 2022/45/B/ST7/03076.