Block diagonal semistability factors and Lyapunov semistability of block triangular matrices
The concepts of Lyapunov diagonal (semi)stability and maximal scaling factors are generalized to block diagonal case. In particular, the following topics are considered. 1. The relation between Lyapunov semistability of a complex matrix and Lyapunov semistability of its diagonal blocks is investigated. 2. Lyapunov block diagonal stability of a matrix is characterized in terms of the diagonal blocks of \(AH+HA^*\) as \(H\) ranges over nonzero positive semidefinite Hermitian matrices. 3. Block triangular matrices with block diagonal semistability factors are characterized in terms of Lyapunov semistability of the diagonal blocks. 4. Block triangular matrices with general semistability factors are studied.
positive semidefinite Hermitian matrices
scientific article; zbMATH DE number 64477
scientific article