Stability of matrices with negative diagonal submatrices

This paper discusses stability conditions for matrices that determine the homogeneous dynamics of systems of linear second-order differential equations. In particular, we focus on situations in which these matrices have a negative diagonal submatrix. We present a number of theorems that provide conditions which are sufficient for either stability or instability of such matrices. In order to discuss the instability theorems and unify them with earlier results, we introduce the concept of the dominant diagonal number of a matrix. (C) 2002 Elsevier Science Inc. All rights reserved.