Specific duality and stability of positive electrical circuits

Open access


The specific duality and asymptotic stability of the positive linear electrical circuits are addressed. The specific duality of positive linear electrical circuits composed of resistances, inductances, capacitances and source voltages is established. 1) The linear electrical circuits are positive if and only if the common branches between meshes with resistances and inductances and meshes with resistances and capacitances contain only source voltages; 2) In linear electrical circuits the interchanges of the inductances by the capacitances and the capacitances by inductances do not change the asymptotic stability of the electrical circuits. The asymptotic stability of the positive and nonpositive electrical circuits is analyzed.

[1] Aracena J., Demongeot J., Goles E., Positive and negative circuits in discrete neural networks, IEEE Trans. Neural Networks, vol. 15, no. 1, pp. 7783 (2004).

[2] Benvenuti L., Farina L., A tutorial on the positive realization problem, IEEE Trans. on Automatic Control, vol. 49, no. 5, pp. 651664 (2004).

[3] Farina L., Rinaldi S., Positive Linear Systems, Theory and Applications, J. Wiley, New York 2000.

[4] Gantmacher F.R., The Theory of Matrices, Chelsea Pub. Comp., London (1959).

[5] Kaczorek T., A class of positive and stable time-varying electrical circuits, Electrical Review, vol. 91, no. 5, pp. 121124 (2015).

[6] Kaczorek T., Constructability and observability of standard and positive electrical circuits, Electrical Review, vol. 89, no. 7, pp. 132136 (2013).

[7] Kaczorek T., Decoupling zeros of positive continuous-time linear systems and electrical circuits, Advances in Systems Science, Advances in Intelligent Systems and Computing, Springer, vol. 240, pp. 115 (2014).

[8] Kaczorek T., Minimal-phase positive electrical circuits, Electrical Review, vol. 92, no. 3, pp. 182189 (2016).

[9] Kaczorek T., Normal positive electrical circuits, IET Circuits Theory and Applications, vol. 9, no. 5, pp. 691699 (2015).

[10] Kaczorek T., Positive 1D and 2D Systems, Springer-Verlag, London (2002).

[11] Kaczorek T., Positive electrical circuits and their reachability, Archives of Electrical Engineering, vol. 60, no. 3, pp. 283301 (2011).

[12] Kaczorek T., Positive fractional linear electrical circuits, Proceedings of SPIE, vol. 8903, Bellingham WA, USA, Art. No 3903-35 (2013).

[13] Kaczorek T., Positive linear systems with different fractional orders, Bull. Pol. Acad. Sci., Technical Sciences, vol. 58, no. 3, pp. 453458 (2010).

[14] Kaczorek T., Positive systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems - regular paper, vol. 58, no. 6, pp. 12031210 (2011).

[15] Kaczorek T., Positive unstable electrical circuits, Electrical Review, vol. 88, no. 5a, pp. 187192 (2012).

[16] Kaczorek T., Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw (in Polish) (1998).

[17] Kaczorek T., Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review, vol. 89, no. 10, pp. 200203 (2013).

[18] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, Springer vol. 13 (2015).

Archives of Electrical Engineering

The Journal of Polish Academy of Sciences

Journal Information

CiteScore 2016: 0.71

SCImago Journal Rank (SJR) 2016: 0.238
Source Normalized Impact per Paper (SNIP) 2016: 0.535

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 225 221 27
PDF Downloads 137 134 22