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Hurwitz
 

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Hurwitz Polynomial




A simple example of a Hurwitz polynomial is the following:

:x^2 + 2x + 1

The only real solution is −1, as it factors to:

:(x+1)^2.

For a polynomial to be Hurwitz, it is necessary but not sufficient that all of its coefficients be positive. For all of a polynomial's roots to lie in the left half-plane, it is necessary and sufficient that the polynomial in question pass the Routh-Hurwitz Stability Criterion .