Journal ArticleDOI
Stability analysis via the extended matrix sign function
R.L. Mattheys
- Vol. 125, Iss: 3, pp 241-243
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In this paper, an extended matrix sign function is proposed and a computational method is given for its evaluation and its application to the stability analysis of linear time-invariant systems is demonstrated.Abstract:
An extended matrix sign function is proposed; a computational method is given for its evaluation and its application to the stability analysis of linear time-invariant systems is demonstrated.read more
Citations
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Journal ArticleDOI
The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)
Journal ArticleDOI
Solving the algebraic Riccati equation with the matrix sign function
TL;DR: In this article, the matrix-sign-function algorithm for algebraic Riccati equations is improved by a simple reorganization that changes nonsymmetric matrix inversions into symmetric matrix inverse inversions.
Journal ArticleDOI
The matrix sign function
Charles Kenney,Alan J. Laub +1 more
TL;DR: A survey of the matrix sign function is presented including some historical background, definitions and properties, approximation theory and computational methods, and condition theory and estimation procedures.
Some properties of matrix sign functions derived from continued fractions
TL;DR: In this article, an alternative representation of a matrix sign function based on an irrational function described by a continued fraction is proposed, and new algorithms for computing the matrix sign functions are developed.
Journal ArticleDOI
Spectral decomposition of a matrix using the generalized sign matrix
Eugene D. Denman,J. Leyva-Ramos +1 more
TL;DR: An algorithm for spectral decomposition is presented which does not require knowledge of eigenvalues and eigenvectors, and a set of Eigenprojectors are defined which covers the entire spectrum of a matrix.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.