Hurwitz matrix

Their definition is related to the associated Hurwitz matrix.

The square Hurwitz matrix associated to P is given below:

A system is stable if its control matrix is a Hurwitz matrix.

Hurwitz matrix is named after Adolf Hurwitz.

Note that it is not necessary that for a specific argument be a Hurwitz matrix - it need not even be square.

In engineering, M-matrices also occur in the problems of feedback control in control theory and is related to Hurwitz matrix.

Related classes are L-matrices, M-matrices, P-matrices, Hurwitz matrices and Metzler matrices.

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.

However, the process is similar for the continuous-time case; the observer gains are chosen to make the continuous-time error dynamics converge to zero asymptotically (i.e., when is a Hurwitz matrix).

The ith Hurwitz determinant is the determinant of the ith principal minor of the above Hurwitz matrix H. There are n Hurwitz determinants for a characteristic polynomial of degree n.