Matlab and Cauchy's Argument Principle: Plot the contour on the s-plane of a transfer Function

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Questions

1. How do I plot the contour of a given Nyquist plot onto the *s-plane of a given transfer function on Matlab?

*s-plane: is the complex plane on which Laplace transforms are graphed. It Has imaginary(vertical) and real(horizontal) axis.


2. How do I plot a function like of that of a parabola shape onto the s-plane(on Matlab but also in general).

2a. What is then the mathematical function look like?


Explanation of Cauchy's Argument Principle:

https://www.youtube.com/watch?v=sof3meN96MA Time code: 4:03 for explanation


I want to compare the plot to its contour s-plane counter part.

This will help better visualize the relationship between a Nyquist plot and it's benefits of using its representation.


I could not find anything on the Matlab Nyquist function page: Nyquist Matlab Function: https://uk.mathworks.com/help/control/ref/nyquist.html