Everything about Hurwitz Polynomial totally explained
In
mathematics, a
Hurwitz polynomial, named after
Adolf Hurwitz, is a
polynomial whose coefficients are positive
real numbers and whose zeros are located in the left half-plane of the
complex plane, that is, the real part of every zero is negative. One sometimes uses the term
Hurwitz polynomial simply as a (real or complex) polynomial with all zeros in the left-half plane (for example, a Hurwitz
stable polynomial).
Examples
A simple example of a Hurwitz polynomial is the following:
»
The only real solution is −1, as it factors to:
»
Properties
For a polynomial to be Hurwitz, it's 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's necessary and sufficient that the polynomial in question pass the
Routh-Hurwitz stability criterion.
A given polynomial can be tested to be Hurwitz or not by using the continued fraction expansion technique.
Further Information
Get more info on 'Hurwitz Polynomial'.
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