Metzler Cyclic Electric Systems

Mitkowski, Wojciech

doi:10.5604/01.3001.0010.4070

Abstract

In applications we meet with positive (nonnegative) systems. A system generated by a linear differential equation with a Metzler-matrix is called a nonnegative system. The paper shows the basic dynamic properties of nonnegative continuous-time systems. Considered was the example of an oscillating electrical circuit with a cyclic Metzler-matrix, enabling the correct physical interpretations.

References

[1] Farina L., Rinaldi S., Positive Linear Systems. Theory and Applications, J. Wiley, New York 2000.10.1002/9781118033029
Search in Google Scholar Back to article
[2] Kaczorek T., Positive linear systems and their relationship with electrical circuits, Proc. of XX SPETO, Gliwice, 1997, Vol. 2, pp. 33-41.
Search in Google Scholar Back to article
[3] Kaczorek T., Positive 1D and 2D Systems, Springer-Verlag, London 2002.10.1007/978-1-4471-0221-2
Search in Google Scholar Back to article
[4] Kaczorek T., Selected Problems in Fractional Systems Theory, Springer-Verlag, 201110.1007/978-3-642-20502-6
Search in Google Scholar Back to article
[5] Kaczorek T., Characteristic polynomials of positive and minimal-phase electrical circuits, Proc. of XXXIX IC-SPETO, Gliwice - Ustroń, 18-21.05.2016, pp. 7-8.
Search in Google Scholar Back to article
[6] Kaczorek T., Rogowski K., Fractional linear systems and electrical circuits, Technical University of Białystok Press, Białystok 2014.10.1007/978-3-319-11361-6
Search in Google Scholar Back to article
[7] Minc H., Nonnegative Matrices, J. Wiley, New York 1988.
Search in Google Scholar Back to article
[8] Mitkowski W., Układy podobne do układów dodatnich, Proc. of XXIII IC-SPETO, Gliwice - Ustroń, 24-27.05.2000, pp. 214-218 [Similar systems to the positive systems - available in Polish].
Search in Google Scholar Back to article
[9] Mitkowski W., Remarks on stability of positive linear systems, ‘Control and Cybernetics’, 2000, Vol. 29, No. 1, pp. 295-304.
Search in Google Scholar Back to article
[10] Mitkowski W., Dynamical properties of Metzler systems, ‘Bulletin of the Polish Academy of Sciences. Technical Sciences’, 2008, Vol. 56, No. 4, pp. 309-312.
Search in Google Scholar Back to article
[11] Mitkowski W., Remarks about fractional Metzler systems, Technical University of Białystok Press, Białystok 2012, pp. 171-180.
Search in Google Scholar Back to article
[12] Mitkowski W., Uwagi o dodatnich obwodach elektrycznych, Proc. of XL IC-SPETO, Gliwice - Ustroń, 17-20.05.2017 [Remarks About Positive Electrical Circuits - available in Polish].
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Metzler Cyclic Electric Systems

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