Hurwitz Polynomial

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 (i.e., a Hurwitz stable polynomial).


A polynomial is said to be Hurwitz if the following conditions are satisfied:

1. P(s) is real when s is real.

2. The roots of P(s) have real parts which are zero or negative.

  • Note: Here P(s) is any polynomial in s.

Read more about Hurwitz Polynomial:  Examples, Properties