赫尔维茨多项式（Hurwitz polynomial）得名自德国数学家阿道夫·赫维兹，是一种特殊的多项式，其系数为正值，而且其根解都在复数平面的左半边或是在虚轴上，也就是根的实部均为负数或是零。有时此一用语会将多项式根的实部限制为只允许负值，也就是解不能在虚轴上（赫尔维茨稳定多项式）。

若以下二个条件皆成立，复变量s 的多项式P(s)为赫尔维茨多项式：

赫尔维茨多项式在控制系统理论中非常重要，其表示稳定线性非时变系统的特征多项式。多项式是否赫尔维茨多项式可以直接求解方程序，或是用劳斯–赫尔维茨稳定性判据求得。

In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose roots (zeros) are located in the left half-plane of the complex plane or on the imaginary axis, that is, the real part of every root is zero or negative. Such a polynomial must have coefficients that are positive real numbers. The term is sometimes restricted to polynomials whose roots have real parts that are strictly negative, excluding the axis (i.e., a Hurwitz stable polynomial).