On the existence of positive diagonalPsuch thatPA + A^{T}P < 0

Given a real square matrix
A
we address the question: Does there exist a positive diagonal matrix
P
such that
PA + A^{T}P
is negative definite? We present an algorithm which when applied to
A
gives a definite yes or no answer to this question. If the answer is yes, the algorithm will provide one such
P
.