Global Stability of Fractional Feedback Systems with Positive Linear Parts

• Autorzy: Kaczorek Tadeusz

Identyfikatory

DOI

10.12716/1001.19.01.39

• Języki publikacji: EN

Abstrakty

EN

The global (absolute) stability of fractional nonlinear systems with negative feedbacks and positive not necessary asymptotically stable linear parts is addressed. It is shown that the coefficients of the transfer matrix of fractional positive asymptotically stable systems are positive. Sufficient conditions for the global stability of the fractional nonlinear systems with positive linear parts are established.

Słowa kluczowe

EN

nonlinear systems; fractional calculus; stability of systems; control systems; positive systems; Lyapunov stability; transfer functions; state-space models

• Wydawca: Faculty of Navigation, Gdynia Maritime University
• Czasopismo: TransNav : International Journal on Marine Navigation and Safety of Sea Transportation
• Rocznik: 2025
• Tom: Vol. 19 No. 1
• Strony: 333--337
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Kaczorek Tadeusz

• Bialystok University of Technology, Białystok, Poland

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

Bibliografia

• [1] Berman A. and Plemmons R.J.: Nonnegative Matrices in the Mathematical Sciences, SIAM, 1994.
• [2] Borawski K.: Modification of the stability and positivity of standard and descriptor linear electrical circuits by state feedbacks, Electrical Review, vol. 93, no. 11, 2017, 176-180.
• [3] Busłowicz M., Kaczorek T.: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. Appl. Math. Comput. Sci., vol. 19, no. 2, 2009, 263-169.
• [4] Farina L., Rinaldi S.: Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [5] Kaczorek T.: 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.
• [6] Kaczorek T.: Analysis of positivity and stability of fractional discrete-time nonlinear systems, Bull. Pol. Acad. Sci. Techn., vol. 64, no. 3, 2016, 491-494.
• [7] Kaczorek T.: Global stability of nonlinear feedback systems with positive linear parts, International Journal of Nonlinear Sciences and Numerical Simulation. 2019 (in Press).
• [8] Kaczorek T.: Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [9] Kaczorek T.: Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, 2010, 453-458.
• [10] Kaczorek T.: Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. on Circuits and Systems, vol. 58, no. 7, 2011, 1203-1210.
• [11] Kaczorek T.: Positive fractional continuous-time linear systems with singular pencils, Bull. Pol. Acad. Sci. Techn., vol. 60, no. 1, 2012, 9-12.
• [12] Kaczorek T.: Descriptor positive nonlinear systems, Advances in Intelligent Systems and Computing, vol. 550, 2017, Springer, 34-44.
• [13] Kaczorek T.: Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
• [14] Kaczorek T.: Stability of fractional positive nonlinear systems, Archives of Control Sciences, vol. 25, no. 4, 2015, 491-496.
• [15] Kaczorek T.: Superstabilization of positive linear electrical circuit by state-feedbacks, Bull. Pol. Acad. Sci. Techn., vol. 65, no. 5, 2017, 703-708.
• [16] Kaczorek T.: Theory of Control, vol. 2, PWN, Warsaw, 1981 (in Polish).
• [17] Kaczorek T., Borawski K.: Stability of Positive Nonlinear Systems, Proc. MMAR 2017, Międzyzdroje, 28-31.08.2017.
• [18] Kudrewicz J.: Ustoicivost nieliniejnych sistem z obratnoj swjazju, Avtomatika i Telemechanika, vol. 25, no. 8, 1964.
• [19] Lyapunov A.M.: Obscaja zadaca ob ustoicivosti dvizenija, Gostechizdat, Moskwa, 1963.
• [20] Leipholz H.: Stability Theory, New York Academic Press, 1970.

Uwagi

1. Pełne imię podano na stronie internetowej czasopisma w "Authors in other databases."

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