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While checking whether the given polynomial is Hurwitz or not, we perform continued fraction expansion. We were taught how to perform this check(i.e) look at the sign of the coefficients of the quotients after performing the normal expansion steps.

I can understand why this method would work for a normal fraction like for example \$158/18\$. But, why separating a single polynomial into odd and even terms and dividing them(and invert and continue) yields all positive terms in the quotients for a Hurwitz polynomial?

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  • $\begingroup$ I'm voting to close this question as off-topic because it’s not an EE question. Try math stack exchange. $\endgroup$ – Andy aka Sep 21 at 8:19
  • $\begingroup$ Are you referring to the Routh-Hurwitz criterion? If so, there are plenty of hits on Google $\endgroup$ – Chu Sep 21 at 8:25
  • $\begingroup$ @Chu Right now, we are being taught two methods to check whether the given polynomial is Hurwitz or not. (1)Routh's array (2)Continued Fraction Expansion(I've a feeling both are the same, though). Whenever I search for math behind Routh's array, I get how the "procedure" but not the math hiding behind. And I couldn'tfind this continued fraction expansion anywhere, and hence I posted $\endgroup$ – Aravindh Vasu Sep 21 at 8:35
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    $\begingroup$ I guess this subject is addressed in complex analysis and control theory. $\endgroup$ – NoChance Sep 21 at 16:55
  • $\begingroup$ @NoChance I couldn't find the math behind it anywhere on the net( always as saw as I could see) $\endgroup$ – Aravindh Vasu Sep 21 at 23:25
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The subject is beyond my knowledge. However, I came across the following proofs, I hope you find any value in either of them.

1-Paper-Elementary proof of the Routh-Hurwitz test by Gjerrit Meinsma

2-paper -A NETWORK PROOF OF A THEOREM ON HURWITZ POLYNOMIALS AND ITS GENERALIZATION - By T. R. BASHKOW and C. A. DESOER

3-Chapter 4 - Page 75 of:

Google Books:A Mathematical Introduction to Control Theory by Shlomo Engelberg

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