Stabilization of matrices
TLDR
In this article, the authors considered the conjecture that given a real nonsingular matrix A, there exists a real diagonal matrix Λ with ¦λ ii λ = 1 and a permutation matrix P such that (ΛPA) is positive stable.About:
This article is published in Linear Algebra and its Applications.The article was published on 1978-09-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Integer matrix & Matrix (mathematics).read more
Citations
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Journal ArticleDOI
Unifying Matrix Stability Concepts with a View to Applications
TL;DR: Multiplicative and additive stability, diagonal stability, Schur stability, and $H$-stability are classical concepts which arise in studying linear dynamical systems and are unified in this article.
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Unifying matrix stability concepts with a view to applications
TL;DR: This work unifies several well-known matrix problems and to consider common methods of their analysis in one concept of $({\mathfrak D}, {\mathcal G}, \circ)$-stability, which depends on a stability region ${\math frak D} \subset {\mathbb C}$, a matrix class ${\ mathcal G}$ and a binary matrix operation $\circ$.
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How to generalize $D$-stability
TL;DR: In this paper, a generalization of multiplicative and additive stability, Schur stability, and hyperbolicity is introduced, which generalizes known definitions of multiplative and additive $D$-stability.
Journal ArticleDOI
Spectral Unmixing of Classes of Arbitrary Nonsingular Matrices
ShiNung Ching,Edward J. Davison +1 more
TL;DR: In this article, it was shown that for any nonsingular matrix M, there exists a finite set of unmixing matrices S such that at least one member Si ϵ S will exhibit the property that MSi will be a Hurwitz matrix.
Book ChapterDOI
Integral Sliding Mode Control of Multi-input Nonlinear Uncertain Non-affine Systems
TL;DR: This chapter is devoted to examine the control of multi-input uncertain non affine systems, which has relatively few contributions and the authors attempt to identify the reasons for this.
References
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Journal ArticleDOI
Some theorems on the inertia of general matrices
TL;DR: In the case of matrix equations, there appears to be only one known general result concerning the location of the eigenvalues of a matrix in the left half-plane as discussed by the authors.
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On the stabilization of matrices and the convergence of linear iterative processes
TL;DR: In this paper, it was shown that if a real square matrix P fulfils certain rather general conditions then there exists a real diagonal matrix D such that the characteristic equation of DP is stable and furthermore, aperiodic.
Journal ArticleDOI
Stabilization by a diagonal matrix
TL;DR: In this paper, it was shown that, given a complex square matrix A all of whose leading principal minors are nonzero, there is a diagonal matrix D such that the product DA of the two matrices has all its characteristic roots positive and simple.
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On the inertia of some classes of partitioned matrices
TL;DR: In this paper, the authors make repeated use of the Sylvester-Hermite theorem that the inertia of a Hermitian matrix remains invariant under a cogredient transformation.