Is there any theoretical or mathematical proof behind Bode and Nyquist stability crit

[mike buba]

Is there any theoretical or mathematical proof behind Bode and Nyquist stability criteria?
Are there any reference materials on this topic?

 

[FvM]

Re: Theory behind Bode and Nyquist stability criteria

Obviously you didn't yet search for previous Edaboard discussions. There are a lot.

 

[mike buba]

Re: Theory behind Bode and Nyquist stability criteria

Obviously you didn't yet search for previous Edaboard discussions. There are a lot.

Well I admit that I did not thoroughly search the forum .

But there are lot’s of answers on how to find phase and gain margin using either mathematical expressions or graphical representations or both.

I am interested in mathematical proof behind all that. How Mr. Bode came up with the expressions for gain margin and phase margin. I imagine there were not based entirely on experimental results, but also on some theorems and lemmas.

 

[The Electrician]

Re: Theory behind Bode and Nyquist stability criteria

Is there any theoretical or mathematical proof behind Bode and Nyquist stability criteria?
Are there any reference materials on this topic?

You could start with the Wikipedia article:

https://en.wikipedia.org/wiki/Nyquist_stability_criterion

Then you could read Nyquist's original paper:

https://www3.alcatel-lucent.com/bstj/vol11-1932/articles/bstj11-1-126.pdf

Bode wrote a book with his work fully explained:

https://www.amazon.com/s/ref=nb_sb_...etwork+analysis+and+feedback+amplifier+design

 

[LvW]

Re: Theory behind Bode and Nyquist stability criteria

Is there any theoretical or mathematical proof behind Bode and Nyquist stability criteria?
Are there any reference materials on this topic?

You should know that the "Bode stability criterion" is nothing else than a visualization of Nyquist`s criterion using a separation between phase and magnitude response.
From the mathematical viewpoint both are equivalent.