Hurwitz Stability of Metzler Matrices

In this note, a simple method is presented that is both necessary and sufficient for determining whether a given Metzler matrix A is Hurwitz. The method is based on the well known fact that a Hurwitz Metzler matrix is also diagonally stable. By using this fact, very simple conditions are derived for the Hurwitz stability of a Metzler matrix. The conditions are stated in terms of the signs of the diagonal entries of a sequence of lower dimensional matrices. The efficacy of the conditions is demonstrated by applying them to determine stability in several examples.