Talk:Routh–Hurwitz stability criterion

i threw together this page really quick, but i didn't have the time (nor do i know enough of the specifics) to flesh it out right now. any help would be appreciated.--Whiteknight 01:53, 10 Jun 2005 (UTC)

Table Method
I've added a table method for higher order polynomials. This method was taught to me as part of my Control and Mechatronics course and referred to as the "Routh-Hurwitz Method". Looking on Wikipedia, I couldn't find a mention of it so I've placed it here. If somebody could clarify if this is the true name, then make the required changes (also the page mentions the Jury Test, but theres nothing here.

Also could someone wikify the table?

And $$D(s)=a_ns^n+a_{n-1}s^{n-1}+...+a_1s+a_0$$ is a latex bug (the '-' shouldn't be there)?


 * It was taught (and I use that term loosly...) as "Routh-Hurwitz tabulation" in my Control course. 122.49.140.246 12:27, 10 November 2006 (UTC)

There's a problem with the table given for the example. It should read:

[  1,   2,   3] [   4,   5,   6] [ 3/4, 3/2,   0] [  -3,   6,   0] [   3,   0,   0] [   6,   0,   0]


 * fixed now, 122.49.140.246 12:23, 10 November 2006 (UTC)

Here is Hurwitz's original publication http://www.gdz-cms.de/index.php?id=img&no_cache=1&IDDOC=36175&IDDOC=36175&branch=&L=1. —Preceding unsigned comment added by 80.218.62.174 (talk) 20:58, 12 November 2007 (UTC)

Appendix A
Appendix A seems to proof "f is stable" from the assumption "f is stable". Seems like a useless statement. Or am I missing the point here?

Haha I don't know what point he is trying to make either. If q = 0, then 2q = 0...Are they joking? I reckon delete too. Jez 006 (talk) 21:40, 19 February 2010 (UTC)

Fourth-order polynomials
For the criteria for a fourth-order polynomial $$a_4 s^4+a_3 s^3+a_2 s^2+a_1 s+a_0$$, the page stated that all coefficients be positive, that $$a_3 a_2>a_4 a_1$$, and that $$a_3 a_2 a_1>a_4 a_1^2 + a_0 a_3^2$$; but all coefficients being positive and $$a_3 a_2 a_1>a_4 a_1^2 + a_0 a_3^2$$ automatically imply that $$a_3 a_2>a_4 a_1 + \frac {a_0 a_3^2} {a_1}$$, so the criterion that $$a_3 a_2>a_4 a_1$$ is redundant. Am I making any mistake, or is there really redundancy in the page? Thanks! --131.111.5.177 (talk) 21:27, 2 March 2016 (UTC)


 * The element for s^4 is now just one so that we do not care that a_4 must be positive and could remove one of the elements. You are mistaken: the bigger statements imply that all elements are positive, okay? Certainly, the smaller creterion is redundent, sure, if we now assume all are positive, as required for any degree polinomial. Valery Zapolodov (talk) 00:51, 19 July 2022 (UTC)

2nd, 3rd, and 4th degree polynomials
The section Routh-Hurwitz stability criterion, which was added in 2011 by a single-edit contributor, cannot be right as stated, because the number of conditions is supposed to equal the degree rather than exceed it. I'm going to correct it in the 2nd and 3rd degree cases. Could someone who knows the 4th degree case check it? Loraof (talk) 22:18, 10 January 2017 (UTC)


 * Seeing no response, I'm going to delete the 4th degree case. Loraof (talk) 17:35, 9 March 2017 (UTC)
 * What? This is this https://www.youtube.com/watch?v=6eZVMftq94w or this https://www.youtube.com/watch?v=QWb9sq35cNk, number of conditons is at least the degree, because all coeff. must be positive, see Lienard-Chipart! Wow. Yes, of curse technically, some of those coeff. > 0 are written inside the bigger statements, and the moment we understand they just be all postive, those are no longer independent. Valery Zapolodov (talk) 23:40, 18 July 2022 (UTC)