Characterizations of classes of stable matrices.
type: Item
instance of: scholarly article
title: Characterizations of classes of stable matrices.
zbMATH Open document ID: 1036.15015
DOI: 10.1016/S0024-3795(03)00558-5
author: D. Massart
published in: Linear Algebra and its Applications
publication date: 2003-11-19T00:00:00Z
review text: Let \({\mathcal J}\subset\mathbb{R}^{n\times n}\) be the set of matrices with eigenvalues in the open right half complex plane. Various subsets of \({\mathcal J}\) are studied, including their characterizations and mutual interrelations. In doing so the set product \({\mathcal M}_1\otimes{\mathcal M}_2= \{M_1M_2: M_i\in{\mathcal M}_i\}\) is systematically used, where \({\mathcal M}_i\subset \mathbb{R}^{n\times n}\). The cases \(n= 2,3\) are considered in particular. In this way the results by \textit{B. Cain}, \textit{L. M. De Alba}, \textit{L. Hogben} and \textit{C. R. Johnson} [Linear Algebra Appl. 268, 151--169 (1998; Zbl 0917.47012)] and \textit{G.-R. Duan} and \textit{R. J. Patton} [Automatica 34, 509--511 (1998; Zbl 0934.93052)] are generalized.
reviewed by: Mihail M. Konstantinov
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 2005998
zbMATH Keywords: matrix stability
zbMATH Keywords: Lyapunov equation
zbMATH Keywords: diagonal stability
zbMATH Keywords: inertia
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005998