Analysis of positivity and stability of time-varying continuous-time linear systems and electrical circuits

• Autorzy: Kaczorek T.
• 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 system are established. It is shown that there exists a large class of positive and asymptotically stable electrical circuits with time-varying parameters. The Lyapunov method is extended to positive nonlinear systems. Examples of positive electrical circuits are presented.

Słowa kluczowe

EN

positive; linear; time-varying; system; electrical circuit; stability; Lyapunov method; test

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Computer Applications in Electrical Engineering
• Rocznik: 2015
• Tom: Vol. 13
• Strony: 1--18
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology 15-351 Bialystok, ul. Wiejska 45D

Bibliografia

• [1] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York 2000.
• [2] Kaczorek T., Controllability and observability of linear electrical circuits, Electrical Review, Vol. 87, No. 9a, pp. 248-254, 2011.
• [3] Kaczorek T., Fractional positive continuous-time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci., Vol. 18, No. 2, pp. 223-228, 2008.
• [4] Kaczorek T., Fractional standard and positive descriptor time-varying discrete-time linear systems, Progress in Automation, Robotics and Measuring Techniques, Vol. 350, Springer International Publishing, pp. 101-112, 2015.
• [5] Kaczorek T., Positive 1D and 2D Systems, Springer Verlag, London 2002.
• [6] Kaczorek T., Positive electrical circuits and their reachability, Archives of Electrical Engineering, Vol. 60, No. 3, pp. 283-301, 2011 and also Selected classes of positive electrical circuits and their reachability, Monograph Computer Application in Electrical Engineering, Poznan University of Technology, Poznan 2012.
• [7] Kaczorek T., Positive descriptor time-varying discrete-time linear systems and their asymptotic stability, TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, Vol. 9, No. 1, pp. 83-89, 2015.
• [8] Kaczorek T., Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems, Vol. 58, No. 6, pp. 1203-1210, 2011.
• [9] Kaczorek T., Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, Vol. 5, No. 2, pp. 42-51, 2011.
• [10] Kaczorek T., Positivity and stability of fractional descriptor time-varying discrete-time linear systems, AMCS, 2015 (in Peress).
• [11] Kaczorek T., Positivity and stability of time-varying discrete-time linear systems, Intelligent Information and Database Systems, Lecture Notes in Computer Science, Vol. 9011, Springer International Publishing, pp. 295-303, 2015.
• [12] Kaczorek T., Stability of positive continuous-time linear systems with delays, Bull. Pol. Acad. Sci. Techn., vol. 57, no. 4, 2009, 395-398.
• [13] Kaczorek T., Stability and stabilization of positive fractional linear systems by state-feedbacks, Bull. Pol. Acad. Sci. Techn., vol. 58, no. 4, 2010, 517-554.
• [14] Kaczorek T., Selected Problems of Fractional System Theory, Springer Verlag 2011.
• [15] Kaczorek T., New stability tests of positive standard and fractional linear systems, Circuits and Systems, no. 2, pp. 261-268, 2011.
• [16] Ostalczyk P., Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Technical University of Lodz Press, Lodz, 2008 (in Polish).
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