Stability of perturbed polynomials based on the argument principle and Nyquist criterion

Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

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A Nyquist criterion for synchronization in networks of heterogeneous linear systems

IFAC Proceedings Volumes ◽

10.3182/20100913-2-fr-4014.00015 ◽

2010 ◽

Vol 43 (19) ◽

pp. 103-108 ◽

Cited By ~ 1

Author(s):

E. Lovisari ◽

U.T. Jonsson

Keyword(s):

Linear Systems ◽

Nyquist Criterion

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Experimental Validation of Harmonic Impedance Measurement and LTP Nyquist Criterion for Stability Analysis in Power Converter Networks

IEEE Transactions on Power Electronics ◽

10.1109/tpel.2018.2880935 ◽

2019 ◽

Vol 34 (8) ◽

pp. 7972-7982 ◽

Cited By ~ 6

Author(s):

Valerio Salis ◽

Alessandro Costabeber ◽

Stephen M. Cox ◽

Francesco Tardelli ◽

Pericle Zanchetta

Keyword(s):

Stability Analysis ◽

Experimental Validation ◽

Impedance Measurement ◽

Power Converter ◽

Nyquist Criterion

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Compressive Sensing: Analysis of Signals in Radio Astronomy

Open Astronomy ◽

10.1515/astro-2017-0165 ◽

2013 ◽

Vol 22 (4) ◽

Author(s):

G. Gaigals ◽

M. Greitāns ◽

A. Andziulis

Keyword(s):

Compressive Sensing ◽

Radio Astronomy ◽

Signal Analysis ◽

Signal Filtering ◽

Nyquist Criterion

AbstractThe compressive sensing (CS) theory says that for some kind of signals there is no need to keep or transfer all the data acquired accordingly to the Nyquist criterion. In this work we investigate if the CS approach is applicable for recording and analysis of radio astronomy (RA) signals. Since CS methods are applicable for the signals with sparse (and compressible) representations, the compressibility of RA signals is verified. As a result, we identify which RA signals can be processed using CS, find the parameters which can improve or degrade CS application to RA results, describe the optimum way how to perform signal filtering in CS applications. Also, a range of virtual LabVIEW instruments are created for the signal analysis with the CS theory.

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