A class of positive and stable time-varying electrical circuits

• Autorzy: Kaczorek T.

Warianty tytułu

PL

O pewnej klasie dodatnich i stabilnych obwodów elektrycznych o zmiennych w czasie parametrach

• Języki publikacji: EN

Abstrakty

EN

The positivity and stability of a class of time-varying continuous-time linear systems and electrical circuits are addressed. Sufficient conditions for the positivity and asymptotic stability of the systems are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

PL

W pracy rozpatrywana jest dodatniość I stabilność asymptotyczna pewnej klasy obwodów elektrycznych o zmiennych w czasie parametrach. Podano warunki dostateczne dodatniości i stabilności asymptotycznej układów i obwodów elektrycznych. Pokazano, że istnieje obszerna klasa dodatnich i stabilnych asymptotycznie obwodów elektrycznych o zmiennych w czasie parametrach. Rozważania zilustrowano przykładami obwodów elektrycznych.

Słowa kluczowe

EN

positive; time-varying; electrical circuit; stability

PL

dodatnie; zmienne w czasie układy liniowe; stabilność

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2015
• Tom: R. 91, nr 5
• Strony: 121--124
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Kaczorek T.

• Politechnika Białostocka, Wydział Elektryczny, ul. Wiejska 45D, 15-351 Białystok

Bibliografia

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• [2] Czornik A. Niezabitowski M., On the stability of discrete time-varying linear systems, Nonlinear Analysis: Hybrid Systems, 9(2013), 27-41.
• [3] Far ina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York 2000.
• [4] Kaczorek T., Controllability and observability of linear electrical circuits, Electrical Review, 87(2011), no. 9a, 248-254.
• [5] Kaczorek T., Fractional positive continuous-time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci., 18 (2008), no. 2, 223-228.
• [6] Kaczorek T., Fractional standard and positive descriptor time-varying discrete-time linear systems, Submitted to Conf. Automation, 2015.
• [7] Kaczorek T., Positive 1D and 2D Systems, Springer Verlag, London 2002.
• [8] Kaczorek T., Positive electrical circuits and their reachability, Archives of Electrical Engineering, 60(2011), no. 3, 283-301 and also Selected classes of positive electrical circuits and their reachability, Monograph Computer Application in Electrical Engineering, Poznan University of Technology, Poznan 2012.
• [9] Kaczorek T., Positive descriptor time-varying discrete-time linear systems and their asymptotic stability, Submitted to Conf. TransNav, 2015.
• [10] Kaczorek T., Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, 58(2011), no. 6, 1203-1210.
• [11] Kaczorek T., Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, 5(2011), no. 2, 42-51.
• [12] Kaczorek T., Positivity and stability of fractional descriptor time-varying discrete-time linear systems, Submitted to AMCS, 2015.
• [13] Kaczorek T., Positivity and stability of time-varying discretetime linear systems, Submitted to Conf. ACIIDS, 2015.
• [14] Kaczorek T., Stability of positive continuous-time linear systems with delays, Bull. Pol. Acad. Sci. Techn., 57(2009), no. 4, 395-398.
• [15] Kaczorek T., Stability and stabilization of positive fractional linear systems by state-feedbacks, Bull. Pol. Acad. Sci. Techn., 58(2010), no. 4, 517-554.
• [16] Kaczorek T., Selected Problems of Fractional System Theory, Springer Verlag 2011.
• [17] Kaczorek T., New stability tests of positive standard and fractional linear systems, Circuits and Systems, 2(2011), 261-268.
• [18] Kaczorek T., Positive and stable time-varying linear systems and electrical circuits, Submitted to Conf. ZKwE, Poznań, 2015.
• [19] Kaczorek T., Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review, 89(2013), no. 10, 200-203.
• [20] Ostalczyk P., Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Technical University of Lodz Press, Lodz, 2008 (in Polish).
• [21] Podlubny I., Fractional Differential Equations, Academic Press, San Diego, 1999.