Exponential decay of transient values in positive nonlinear systems

• Autorzy: Kaczorek Tadeusz

Identyfikatory

DOI

10.24425/bpasts.2024.151050

• Języki publikacji: EN

Abstrakty

EN

The exponential decay of transient values in nonlinear continuous-time standard and fractional orders with linear dynamical positive feedback systems and of positive linear parts is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. Procedures for the computation of gains characterizing the class of nonlinear elements are given and illustrated in simple examples.

Słowa kluczowe

EN

exponential decay; transient value; fractional order; positive nonlinear dynamical feedback system

PL

wartość przejściowa; rząd ułamkowy; dodatni nieliniowy układ sprzężenia zwrotnego dynamicznego; prawo rozpadu naturalnego

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2024
• Tom: Vol. 72, nr 5
• Strony: art. no. e151050
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Kaczorek Tadeusz

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

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

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, New York: J. Wiley, 2000.
• [3] T. Kaczorek, Selected Problems of Fractional Systems Theory, Berlin: Springer 2011.
• [4] T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits, Cham: Springer 2015.
• [5] W. Mitkowski, “Dynamical properties of Metzler systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 56, no. 4, pp. 309–312, 2008.
• [6] L. 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, doi: 10.1515/bpasts-2017-0076.
• [7] P. Ostalczyk, Discrete Fractional Calculus, River Edgle, NJ: World Scientific, 2016.
• [8] I. Podlubny, Fractional Differential Equations, San Diego, USA: Academic Press, 1999.
• [9] T. Kaczorek, “Absolute stability of a class of fractional positive nonlinear systems,” Int. J. Appl. Math. Comput. Sci., vol. 29, no. 1, pp. 93–98, 2019, doi: 10.2478/amcs-2019-0007.
• [10] T. Kaczorek, “Analysis of positivity and stability of fractional discrete-time nonlinear systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 64, no. 3, pp. 491–494, 2016, doi: 10.1515/bpasts-2016-0054.
• [11] T. Kaczorek, “Global stability of nonlinear feedback systems with fractional positive linear parts,” Int. J. Appl. Math. Comput. Sci., vol.30, no.3, pp. 493–499, 2020, doi: 10.34768/amcs-2020-0036.
• [12] T. Kaczorek, “Global stability of positive standard and fractional nonlinear feedback systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 68, no.2, pp. 285–288, 2020, doi: 10.24425/bpasts.2020.133112.
• [13] T. Kaczorek, “Global stability of nonlinear feedback systems with positive linear parts,” Int. J. Nonlinear Sci. Num. Simul., vol. 20, no 5, pp. 575–579, 2019, doi: 10.1515/ijnsns-2018-0189.
• [14] T. Kaczorek, “Positive linear systems with different fractional orders,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 58, no. 3, pp. 453–458, 2010, doi: 10.2478/v10175-010-0043-1.
• [15] T. Kaczorek, “Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circ. Syst., vol. 58, no. 6, pp. 1203–1210, 2011, doi: 10.1109/TCSI.2010.2096111.
• [16] T. Kaczorek, “Stability of fractional positive nonlinear systems,” Arch. Control Sci., vol. 25, no. 4, pp. 491–496, 2015, doi: 10.1515/acsc-2015-0031.
• [17] T. Kaczorek and A. Ruszewski, “Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks,” Arch. Control Sci., vol. 30, no. 4, pp. 667–681, 2020, doi: 10.24425/acs.2020.135846.
• [18] A. Ruszewski, “Stability of discrete-time fractional linear systems with delays,” Arch. Control Sci., vol. 29, no. 3, pp. 549–567, 2019, doi: 10.24425/acs.2019.130205.
• [19] A.M. Lyapunov, Obscaja zadaca ob ustoicivosti dvizenija, Gostechizdat, Moskwa, 1963 (in Russian).
• [20] H. Leipholz, Stability Theory, New York Academic Press, 1970.