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The Implicit McMillan degree and network descriptions

Livada, M. ORCID: 0000-0002-0432-872X & Leventides, J. (2022). The Implicit McMillan degree and network descriptions. IMA Journal of Mathematical Control and Information, doi: 10.1093/imamci/dnac012


The paper addresses the problem of evaluating the Implicit McMillan degreeδm of W−1(s)⁠, where W−1(s) denotes the transfer function of a passive RLC electrical network. The Implicit McMillan degreeδm specifies the minimum number of dynamic elements needed to completely characterize the passive RLC network, i.e. an electrical network that contains only passive elements (capacitors, inductors and resistors) and associates it with the rank properties of the passive element matrices. A fact that in the circuit literature is intuitively accepted but not rigorously proved is that this degree must be equal to the minimum number of independent dynamical elements in the network Livada (2017, Implicit network descriptions of RLC networks and the problem of re engineering. Ph.D. Thesis, City, University of London) and Leventides et al. (2014, McMillan degree of impedance, admittance functions of RLC networks. In 21st International Symposium on Mathematical Theory of Networks and Systems. The Netherlands: Groningen). In this paper, we investigate this finding, showing that the maximum possible Implicit McMillan degreeδm of such networks is given by rankL+rankC and that this value is reached when certain necessary and sufficient conditions are satisfied.

Publication Type: Article
Additional Information: This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Mathematical Control and Information following peer review. The version of record Maria Livada, John Leventides, The Implicit McMillan degree and network descriptions, IMA Journal of Mathematical Control and Information is available online at:
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Engineering
[img] Text - Accepted Version
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