Global stability of nonlinear feedback systemswith positive descriptor linear parts

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/bpas.2019.127337

• Języki publikacji: EN

Abstrakty

EN

The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f (e) of the nonlinear parts satisfy the condition k₁e ≤ f (e) ≤ k2e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (– 1/k1, – 1/k2).

Słowa kluczowe

EN

global stability; positive descriptor; nonlinear; feedback system

PL

globalna stabilność; nieliniowość; system informacji zwrotnej

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 1
• Strony: 45--51
• Opis fizyczny: Bibliogr. 20 poz., wykr.

Twórcy

autor

Kaczorek T.

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

Bibliografia

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• [3] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London 2000.
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• [6] T. Kaczorek, “Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems, Computational Problems of Electrical Engineering, vol. 5, no. 1, 2015, 11‒16.
• [7] T. Kaczorek, “Superstabilization of positive linear electrical circuit by state-feedbacks”, Bull. Pol. Ac.: Tech., 65 (5), 703‒708 (2017).
• [8] T. Kaczorek, Theory of Control, vol. 2, PWN, Warsaw, 1981 (in Polish).
• [9] T. Kaczorek and K. Borawski, “Stability of Positive Nonlinear Systems”, Proc. MMAR 2017, Międzyzdroje, 28‒31.08.2017.
• [10] A.M. Lyapunov, Obscaja zadaca ob ustoicivosti dvizenija, Gostechizdat, Moskwa, 1963.
• [11] H. Leipholz, Stability Theory, New York Academic Press, 1970.
• [12] M. Busłowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci., 19 (2), 263‒169 (2009).
• [13] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Ac.: Tech., 64 (3), 491‒494 (2016).
• [14] T. Kaczorek, “Stability of fractional positive nonlinear systems”, Archives of Control Sciences, 25 (4), 491‒496 (2015).
• [15] T. Kaczorek, Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin 2011.
• [16] T. Kaczorek, “Descriptor positive nonlinear systems”, Advances in Intelligent Systems and Computing, 550, 34‒44 (2017).
• [17] T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac.: Tech., 60 (1), 9‒12 (2012).
• [18] K. Borawski, “Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks”, Electrical Review, 93 (11), 176‒180 (2017).
• [19] T. Kaczorek, “Global stability of nonlinear feedback systems with positive linear parts” International Journal of Nonlinear Sciences and Numerical Simulation 2018 (under review).
• [20] J. Kudrewicz, „Ustoicivost nieliniejnych sistem z obratnoj swjazju”, Avtomatika i Telemechanika, 25 (8), 1964.

Uwagi

EN

This work was supported by National Science Centre in Poland under work No. 2017/27/B/ST7/02443.

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).