Positive and stable electrical circuits with state-feedbacks

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.24425/123663

• Języki publikacji: EN

Abstrakty

EN

The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of an electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.

Słowa kluczowe

EN

positivity; stability; linear; electrical circuit; state-feedback

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2018
• Tom: Vol. 67, nr 3
• Strony: 563--–578
• Opis fizyczny: Bibliogr. 16 poz., rys., wz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering University of Technology Wiejska 45D, 15-351 Bialystok

Bibliografia

• [1] Ait Rami M., Tadeo F., Controller Synthesis for Positive Linear Systems With Bounded Controls, IEEE Transactions on Circuits and Systems, vol. 54, no. 2, pp. 151–155 (2007).
• [2] Boyd S., El Ghaoui L., Feron E., Balakrishnan V., Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics (SIAM) (1994).
• [3] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications, J. Wiley, New York (2000).
• [4] Kaczorek T., A class of positive and stable time-varying electrical circuits, Electrical Review, vol. 91, no. 5, pp. 121–124 (2015).
• [5] Kaczorek T., Constructability and observability of standard and positive electrical circuits, Electrical Review, vol. 89, no. 7, pp. 132–136 (2013).
• [6] Kaczorek T., Decoupling zeros of positive continuous-time linear systems and electrical circuits, Advances in Systems Science, Advances in Intelligent Systems and Computing, vol. 240, pp. 1–15, Springer (2014).
• [7] Kaczorek T., Infinite eigenvalue assignment by output-feedback for singular systems, Int. J. Appl. Math. Comput. Sci., vol. 14, no. 1, pp. 19–23 (2004).
• [8] Kaczorek T., Minimal-phase positive electrical circuits, Electrical Review, vol. 92, no. 3, 182–189 (2016).
• [9] Kaczorek T., Normal positive electrical circuits, IET Circuits Theory and Applications, vol. 9, no. 5, pp. 691–699 (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. 283–301 (2011).
• [12] Kaczorek T., Positive fractional linear electrical circuits, Proceedings of SPIE, vol. 8903, no 3903–35, Bellingham WA, USA (2013).
• [13] Kaczorek T., Positive unstable electrical circuits, Electrical Review, vol. 88, no. 5a, pp. 187–192 (2012).
• [14] Kaczorek T., Zeroing of state variables in descriptor electrical circuits by state-feedbacks, Electrical Review, vol. 89, no. 10, pp. 200–203 (2013).
• [15] Kaczorek T., Borawski K., Stability of continuous-time and discrete-time linear systems with inverse state matrices, Measurement Automation Monitoring, vol. 62, no. 4, pp. 132–135 (2016).
• [16] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, vol. 13, Springer (2015).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).