In mathematics, a square matrix A is called a Hurwitz matrix if all eigenvalues of A have strictly negative real part, that is,
![\Re[\lambda_i] < 0\,](a/../upload/math/af759c4041aa8dc305c1cf787f22c239.png)
for each eigenvalue λi. A is also called a stability matrix, because then the differential equation
is stable, that is, 
as 
If G(s) is a (matrix-valued) transfer function, then G is called Hurwitz if the poles of all elements of G have negative real part. Note that it is not necessary that G(s), for a specific argument s, be a Hurwitz matrix — it need not even be square. The connection is that if A is a Hurwitz matrix, then the dynamical system
has a Hurwitz transfer function.
References
- Hassan K. Khalil (2002). Nonlinear Systems. Prentice Hall.