Title

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

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2021

Volume

69

Issue

2

Affiliation

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

Authors

Kaczorek, Tadeusz

Keywords

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

Divisions of PAS

Nauki Techniczne

Coverage

e136729

Bibliography

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.

Date

08.03.2021

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.136729

Source

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2021; 69; 2; e136729