Application of the Lagrange-Sylvester formula to computation of the solution to state equations of fractional linear systems

• Autorzy: Kaczorek Tadeusz

Identyfikatory

DOI

10.24425/bpasts.2021.136729

• Języki publikacji: EN

Abstrakty

EN

The Lagrange-Sylvester formula is applied to the computation of the solutions of state equations of fractional continuous-time and discrete-time linear systems. The solutions are given as finite sums with their numbers of components equal to the degrees of the minimal characteristics polynomials of state matrices of the systems. Procedures for computations of the solutions are given and illustrated by numerical examples of continuous-time and discrete-time fractional linear systems.

Słowa kluczowe

EN

computation; solution; formula Lagrange-Sylvester; fractional; continuous-time; discrete-time; linear; system

PL

obliczenia; rozwiązanie; formuła Lagrange-Sylvester; czas ciągły; czas dyskretny; liniowy; system

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2021
• Tom: Vol. 69, nr 2
• Strony: art. no. e136729
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kaczorek Tadeusz

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

Bibliografia

• [1] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, vol. 204, Elsevier Science Inc, New York, 2006.
• [2] P. Ostalczyk, Discrete Fractional Calculus, World Scientific, River Edgle, NJ, 2016.
• [3] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
• [4] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.
• [5] T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits, Springer, Cham, 2015.
• [6] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Acad. Sci. Tech. Sci. 64(3), 491‒494 (2016).
• [7] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Acad. Sci. Tech. Sci. 58(3), 453‒458 (2010).
• [8] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders”, IEEE Trans. Circuits Syst. 58(7), 1203‒1210 (2011).
• [9] T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Acad. Sci. Tech. Sci. 60(1), 9‒12 (2012).
• [10] T. Kaczorek, “Stability of fractional positive nonlinear systems”, Arch. Control Sci. 25(4), 491‒496 (2015).
• [11] A. Ruszewski, “Stability of discrete-time fractional linear systems with delays”, Arch. Control Sci. 29(3), 549‒567 (2019).
• [12] A. Ruszewski, “Practical and asymptotic stabilities for a class of delayed fractional discrete-time linear systems”, Bull. Pol. Acad. Sci. Tech. Sci. 67(3), 509‒515 (2019).
• [13] Ł. Sajewski, “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller”, Bull. Pol. Acad. Sci. Tech. Sci. 65(5), 709‒714 (2017).
• [14] Ł. Sajewski, “Decentralized stabilization of descriptor fractional positive continuous-time linear systems with delays”, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Międzyzdroje, Poland, 2017, pp. 482‒487.
• [15] F.R. Gantmacher, The Theory of Matrices, London: Chelsea Pub. Comp., 1959.
• [16] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, Scientific and Technical Publishing, WNT, Warsaw, 1998.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).