Descriptor continuous- and discrete-time linear systems with zero transfer matrices

• Autorzy: Kaczorek Tadeusz , Klamka Jerzy , Dzieliński Andrzej

Identyfikatory

DOI

10.24425/bpasts.2024.152710

• Języki publikacji: EN

Abstrakty

EN

In this paper, necessary and sufficient conditions for zeroing of the transfer matrices of descriptor continuous-time and discrete-time linear systems are established. The conditions are illustrated by simple numerical examples of the descriptor continuous-time and discrete-time linear systems. Also some remarks on the systems with delays in control are given.

Słowa kluczowe

EN

controllability; observability; zero transfer matrix; discrete-time linear system; continuous-time linear system; descriptor linear systems

PL

sterowalność; obserwowalność; macierz transferu; układ czasu dyskretnego; układ czasu ciągłego; liniowy układ deskryptorowy

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2025
• Tom: Vol. 73, nr 2
• Strony: art. no. e152710
• Opis fizyczny: Bibliogr. 15 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

• Polish Academy of Sciences, Institute of Theoretical and Applied Informatics, 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

• [1] Liyi Dai, Singular Control Systems, Springer Berlin, Heidelberg, 1989.
• [2] Guang-Ren Duan, Analysis and Design of Descriptor Linear Systems, Springer New York, 2010.
• [3] T. Kaczorek, Linear control systems, Wiley, 1992.
• [4] T. Kaczorek, “Zeroing the transfer function matrix of the Roesser model of 2-d linear systems,” Int. J. Appl. Math. Comput. Sci., vol. 33, no. 4, pp. 513–519, 2023.
• [5] T. Kaczorek and K. Borawski, Descriptor Systems of Integer and Fractional Order, Springer, 2021.
• [6] 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.
• [7] T. Kaczorek, J. Klamka, and A. Dzieliński, “Controllability of linear convex combination of linear discrete-time fractional systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 70, no. 5, pp. 1–6, 2022.
• [8] T. Kaczorek, J. Klamka, and A. Dzieliński, “Controllability and observability of the descriptor linear systems reduced to the standard ones by feedbacks,” Acta Mech. Automatica, vol. 18, no. 1, pp. 119–122, 2023.
• [9] R.E. Kalman, “On the general theory of control systems,” in Proceedings of the 1st IFAC Congress on Automatic Control, pp. 481–492. IFAC, 1960.
• [10] R.E. Kalman, “Mathematical description of linear dynamical systems,” SIAM J. Control-Series A, vol. 1, no. 2, pp. 152–192, 1963.
• [11] J. Klamka, “Controllability of dynamical systems – a survey,” Arch. Control Sci., vol. 2, no. 3-4, pp. 281–307, 1993.
• [12] J. Klamka, “Controllability of dynamical systems. A survey,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 61, no. 2, pp. 221–229, 2013.
• [13] J. Klamka, Controllability and Minimum Energy Control, Studies in Systems, Decision, and Control. Springer, 2018.
• [14] A.P. Mercorelli, “Theoretical dynamical noninteracting model for general manipulation systems using axiomatic geometric structures,” Axioms, vol. 11, no. 7, pp. 1–24, 2022.
• [15] L. Pandolfi, “On the zeros of transfer functions of delayed systems,” Syst. Control Lett., vol. 1, no. 3, pp. 204–210, 1981.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).