Block diagonal semistability factors and Lyapunov semistability of block triangular matrices
type: Item
instance of: scholarly article
title: Block diagonal semistability factors and Lyapunov semistability of block triangular matrices
zbMATH Open document ID: 0756.15025
DOI: 10.1016/0024-3795(92)90015-3
author: Daniel Hershkowitz
author: Dafna Shasha
author: David H. Carlson
published in: Linear Algebra and its Applications
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 64477
zbMATH Keywords: Lyapunov diagonal (semi)stability
zbMATH Keywords: maximal scaling
zbMATH Keywords: complex matrix
zbMATH Keywords: Lyapunov block diagonal stability
zbMATH Keywords: positive semidefinite Hermitian matrices
zbMATH Keywords: Block triangular matrices
zbMATH Keywords: Lyapunov semistability
reviewed by: M. Erol Sezer
MaRDI profile type: Publication
full work available at URL: 0024-3795(92)90015-3
OpenAlex ID: W2039928461
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description: scientific article; zbMATH DE number 64477