Maximal Lyapunov scaling factors and their applications in the study of Lyapunov diagonal semistability of block triangular matrices (Q1122634)

This paper introduces the concept of maximal Lyapunov scaling factor for Lyapunov diagonally semistable (LDSS) matrices, and applies it to characterization of block triangular LDSS matrices. The basic definitions and the main result are as follows: - A real square matrix A is LDSS if there exists a positive definite diagonal matrix D such that \(AD+DA^ T\) is positive semidefinite. - A positive definite diagonal matrix D is a maximal Lyapunov scaling factor of a LDSS matrix A if range of \(AD+DA^ T\) is of maximal dimension. - A block triangular matrix is LDSS if and only if every \(2\times 2\) block principal submatrix of it is LDSS.