The generalized Nyquist stability criterion

Question

Khaled Abojlala 2017-8-16

1
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https://ww2.mathworks.cn/matlabcentral/answers/352984-the-generalized-nyquist-stability-criterion

回答： Mitul Saini 2018-5-12

采纳的回答： Mohamed Belkhayat

Hi I am trying to plot the Nyquist plot of MIMO system. any help please

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Answer 1

Mohamed Belkhayat 2017-10-30

5
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https://ww2.mathworks.cn/matlabcentral/answers/352984-the-generalized-nyquist-stability-criterion#answer_288584

Gnyquist.m

Once you have a MIMO matrix transfer function you can generate the plot by finding the eigenvalues of the matrix as a function of frequency. A 2x2 MIMO matrix transfer function will have 2 eigenvalues at every frequency point. The imaginary vs. the real part of the two eigenvalues will yield two loci that should always connect. This is the generalized Nyquist. I include a sample code for a textbook example in Multivariable Feedback Design by Maciejowski. Example 2.7. This example is limited to 2x2 but can be extended easily to higher dimensions.