Eigenvalues assignment in descriptor linear systems by state and its derivative feedbacks

• Autorzy: Kaczorek Tadeusz

Identyfikatory

DOI

10.24425/bpasts.2023.145765

• Języki publikacji: EN

Abstrakty

EN

The eigenvalues assignment problems for descriptor linear systems with state and its derivative feedbacks are considered herein. Necessary and sufficient conditions for the existence of solutions to the problems are established. The Euler and Tustin approximations of the continuous-time systems are analyzed. Procedures for computation of the feedbacks are given and illustrated by numerical examples.

Słowa kluczowe

EN

eigenvalue assignment; descriptor; linear system; state derivative; feedback

PL

przypisanie wartości własnej; deskryptor; układ liniowy; pochodna stanu; informacja zwrotna

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 5
• Strony: art. no. e145765
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Kaczorek Tadeusz

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

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

Bibliografia

• [1] I. Dai, Singular Control Systems, Lectures Notes in Control and Information Sciences. Berlin, 1989.
• [2] D. Guang-Ren, Analysis and Design of Descriptor Linear Systems, New York, USA: Springer, 2010.
• [3] T. Kaczorek, Linear Control Systems, vol. 1 and 2, New York, USA: Research Studies Press LTD, J.Wiley, 1992.
• [4] T. Kaczorek and K. Borawski, “Descriptor Systems of Integer and Fractional Orders,” in Studies in Systems, Decision and Control, Switzerland: Springer Cham, 2021
• [5] T. Kaczorek and A. Ruszewski, “Global stability of discrete-time nonlinear systems with descriptor and fractional positive linear parts and scalar feedbacks, Arch. Control Sci., vol. 30, no. 4, pp. 667–681, 2020.
• [6] T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits, Springer Cham, 2014.
• [7] J. Kalman, “Mathematical description of linear dynamical systems,” J. Soc. Ind. Appl. Math. Ser. A Control, vol. 1, no. 2, pp. 152–192, 1963.
• [8] J. Klamka, “Controllability and Minimum Energy Control, Studies in Systems,” in Decision and Control, vol. 162, Springer Verlag, 2018.
• [9] V. Kucera and P. Zagalak, “Fundamental theorem of state feedback for singular systems,” Automatica, vol. 24, no. 5, pp. 653–658, 1988.
• [10] F.L. Lewis, “A survey of linear singular systems”, Circ. Syst. Signal Proc., vol. 5, no. 1, pp. 1–36, 1986.
• [11] D.G. Luenberger, “Time-invariant descriptor systems”, Automatica, vol. 14, pp. 473–480, 1978.
• [12] D.G. Luenberger, “Dynamic equations in descriptor form,”, IEEE Trans. Autom. Control, vol. 22, no. 3, pp. 312–321, 1977.
• [13] W. Mitkowski, Outline of Control Theory, Krakow, Poland: Publishing House AGH, 2019.
• [14] 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., vol. 65, no. 5, pp. 709714, 2017.
• [15] E. Virnik, “Stability analysis of positive descriptor systems,” Linear Alg. Appl., vol. 429, pp. 2640–2659, 2008.
• [16] S. Żak, Systems and Control, New York, USA: Oxford University Press, 2003.

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).