Characterizations of classes of stable matrices.
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.
scientific article; zbMATH DE number 2005998