Properties
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. A given polynomial can be tested to be Hurwitz or not by using the continued fraction expansion technique.
1. All the poles and zeros of a function are in the left half plane or on its boundary the imaginary axis. 2. Any poles and zeros on the imaginary axis are simple (have a multiplicity of one). 3. Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative. 4. Over the right half plane, the minimum value of the real part of a PR function occurs on the imaginary axis (because the real part of an analytic function constitutes a harmonic function over the plane, and therefore satisfies the maximum principle). 5. there have no any missing term of 's'but it possible after the testing the prf stability
Read more about this topic: Hurwitz Polynomial
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