Global stability of positive standard and fractional nonlinear feedback systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/bpasts.2020.133112

• Języki publikacji: EN

Abstrakty

EN

The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.

Słowa kluczowe

EN

global stability; fractional order; positive; nonlinear system

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2020
• Tom: Vol. 68, nr 2
• Strony: 285--288
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
• [2] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [3] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [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] P. Ostalczyk, Discrete Fractional Calculus, World Scientific, River Edgle, NJ 2016.
• [7] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego 1999.
• [8] 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).
• [9] T. Kaczorek, “Absolute stability of a class of fractional positive nonlinear systems”, Int. J. Appl. Math. Comput. Sci. 29 (1), 93–98 (2019).
• [10] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems”, Bull. Pol. Ac.: Tech. 64 (3), 491–494 (2016).
• [11] T. Kaczorek, “Positive linear systems with different fractional orders”, Bull. Pol. Ac.: Tech. 58 (3), 453–458 (2010).
• [12] T. Kaczorek, ‘‘Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac.: Tech. 60 (1), 9–12 (2012).
• [13] W. Mitkowski, “Dynamical properties of Metzler systems”, Bull. Pol. Ac.: Tech. 56 (4), 309–312 (2008).
• [14] A. Ruszewski, “Stability conditions for fractional discrete-time state-space systems with delays”, 24th Intern. Conf. Methods and Models in Automation and Robotics, Mi ̨ edzyzdroje, Poland 2019.
• [15] 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, 482–487.
• [16] Ł. Sajewski, “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller”, Bull. Pol. Ac.: Tech. 65 (5), 709–714 (2017).
• [17] 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).
• [18] T. Kaczorek and K. Borawski, “Stability of positive nonlinear systems”, 22nd Intern. Conf. Methods and Models in Automation and Robotics, Mi ̨edzyzdroje, Poland 2017.
• [19] J. Kudrewicz, “Stability of nonlinear feedback systems”, Avtomatika i Telemechanika 25 (8), 1964 (in Russian).
• [20] T. Kaczorek, “Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems”, Computational Problems of Electrical Engineering 5 (1), 11–16 (2015).
• [21] T. Kaczorek, “Global stability of nonlinear feedback systems with positive linear parts”, Intern. J. of Nonlinear Sciences and Numerical Simulation 20 (5), 575–579 (2019).
• [22] A.M. Lyapunov, General problem of stable movement, Gostechizdat, Moskwa, 1963 (in Russian).
• [23] H. Leipholz, Stability Theory, New York Academic Press, 1970.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).