Computation of transition matrices of positive linear electrical circuits
DOI:
https://doi.org/10.24136/atest.2019.147Keywords:
positive, linear, electrical circuits, calculation, transition matrixAbstract
A method is proposed for calculation of transition matrices of positive electrical circuits. It is shown that if the transition matrix is presented as finite series of the Metzler matrix with real distinct eigenvalues then the coefficients of the series are nonnegative function of time. The method is applied to positive linear electrical circuits.
Downloads
References
L. Benvenuti, L. Farina, "A tutorial on the positive realization problem," IEEE Trans. on Automatic Control, vol. 49, no. 5, pp. 651-664, 2004.
L. Farina, S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
F.R. Gantmacher, The Theory of Matrices. Chelsea Pub. Comp., London, 1959.
T. Kaczorek, "A class of positive and stable time-varying electrical circuits," Electrical Review, vol. 91, no. 5, pp. 121-124, 2015.
T. Kaczorek, "Constructability and observability of standard and positive electrical circuits," Electrical Review, vol. 89, no. 7, pp. 132-136, 2013.
T. Kaczorek, "Decoupling zeros of positive continuous-time linear systems and electrical circuits," Advances in Systems Science, vol. 240, pp. 1-15, 2014.
T. Kaczorek, "Minimal-phase positive electrical circuits," Electrical Review, vol. 92, no. 3, pp. 182-189, 2016.
T. Kaczorek, "Normal positive electrical circuits," IET Circuits Theory and Applications, vol. 9, no. 5, pp. 691-699, 2015.
T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 200
T. Kaczorek, "Positive electrical circuits and their reachability," Archives of Electrical Engineering, vol. 60, no. 3, pp. 283-301, 2011.
T. Kaczorek, "Positive fractional linear electrical circuits," Proceedings of SPIE, vol. 8903, Bellingham WA, USA, Art. No 3903-35.
T. Kaczorek, "Positive linear systems with different fractional orders.," Bull. Pol. Acad. Sci. Techn., vol. 58, no. 3, pp. 453-458, 2010.
T. Kaczorek, "Positive systems consisting of n subsystems with different fractional orders," IEEE Trans. Circuits and Systems – regular paper, vol. 58, no. 6, pp. 1203-1210, June 2011.
T. Kaczorek, "Positive unstable electrical circuits," Electrical Re-view, vol. 88, no. 5a, pp. 187-192, 2012.
T. Kaczorek, Vectors and Matrices in Automation and Electro-technics, WNT, Warsaw, 1998 (in Polish).
T. Kaczorek, "Zeroing of state variables in descriptor electrical circuits by state-feedbacks," Electrical Review, vol. 89, no. 10, pp. 200-203, 2013.
T. Kaczorek, K. Rogowski, Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, vol. 13, Springer, 2015.