Hurwitz matrix

In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients of a real polynomial.

Namely, given a real polynomial

the ${\displaystyle n\times n}$ square matrix

is called Hurwitz matrix corresponding to the polynomial ${\displaystyle p}$. It was established by Adolf Hurwitz in 1895 that a real polynomial is stable (that is, all its roots have strictly negative real part) if and only if all the leading principal minors of the matrix ${\displaystyle H(p)}$ are positive:

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