Stability of matrices with sufficiently strong negative-dominant-diagonal submatrices

A well-known sufficient condition for stability of a system of linear first-order differential equations is that the matrix of the homogeneous dynamics has a negative dominant diagonal. However, this condition cannot be applied to systems of second-order differential equations. In this paper we introduce the concept of a (negative) dominant diagonal with a given strength factor. Using this, we present stability theorems which show that second-order systems are stable if the matrix of the homogeneous dynamics has submatrices with a sufficiently strong negative dominant diagonal. (C) Elsevier Science Inc., 1997.