# The Basics of the Nyquist Stability Criterion

Explanation 4 resources
Last Edited: 10/27/2023

The Nyquist Stability Criterion can be a bit confusing and daunting when you're first learning it.  This journey is set up to provide the basics in a straightforward and understandable way.  Once you understand these basics, you'll have a good foundation to build on.  This journey is broken up into several sections:

1. Prerequisites - the information you might need before starting this journey
2. Introduce the basic concepts - an overview of the criterion with minimal mathematics
3. Fundamentals - A more mathematically rigorous approach to the criterion

Prerequisite - If you don't have a lot of experience with the Nyquist plot, then it might be useful to review the three major LTI plotting techniques first: Nichols chart, Bode plot, and Nyquist plot. If you understand the basics of the Nyquist plot then you can skip this resource.

## Control Systems in Practice, Part 10: Nichols Chart, Nyquist Plot, and Bode ...

18 min
Beginner
Video
Theory

Explore three popular methods to visualize the frequency response of a linear time-invariant (LTI) system: the Nichols chart, the Nyquist plot, and the Bode plot. Learn about each method...

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Introduce the basic concepts - This video provides a gentle introduction to the Cauchy Argument Principle and shows an animation that I think will help the Nyquist Stability Criterion make more sense (part 1).

## Nyquist Stability Criterion, Part 1

16 min
Beginner
Video
Theory

An explanation of the Nyquist Stability Criterion. This video steps through the importance of the criterion, how to interpret the Nyquist plot graphically, and why it is the way it is....

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Introduce the basic concepts - This is a continuation of the above video.

## Nyquist Stability Criterion, Part 2

18 min
Beginner
Video
Theory

An explanation of the Nyquist Stability Criterion part 2. This video steps through the how to sketch a Nyquist plot by hand, what to do if there are open loop pools on the imaginary axis...

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Fundamentals - If you'd like to see a more rigourous explanation of the criterion the Wikipedia article is actually pretty great.  Hopefully, after the above resources the mathematics will make more sense.

## Nyquist Stability Criterion

15 min
Beginner
Article / Blog
Theory

The Wikipedia article on Nyquist Stability Criterion.  This covers the Nyquist plot, the Cauchy argument principle, and the stability criterion itself.  A mathematical derivation is also...

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