On the positive stability of P2-matrices

In this paper, we study the positive stability of P-matrices. We prove that a matrix A is positive stable if A is a P2P2-matrix and there is at least one nested sequence of principal submatrices of A each of which is also a P2P2-matrix. This result generalizes the result by Carlson which shows the positive stability of sign-symmetric P-matrices and the result by Tang, Simsek, Ozdaglar and Acemoglu which shows the positive stability of strictly row (column) square diagonally dominant for every order of minors P-matrices.