A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1982 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Algebraic Discrete Methods, volume 3, pages 293-304 (issn: 0196-5212, eissn: 2168-345X,

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Authors: Carlson, David; Datta, B. N.; Johnson, Charles R.;

doi: 10.1137/0603030

A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices

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Abstract

Summary: A new necessary and sufficient condition is given for an $n\times n$ complex matrix A to be stable. It involves a positive semi-definite image under a Lyapunov map and the real and imaginary parts of A. This condition is then used to characterize the real tridiagonal matrices which are D-stable, and those which are totally D-stable.

Keywords

D-stability, tridiagonal matrices, semi-definite Lyapunov theorem, Inequalities involving eigenvalues and eigenvectors

15 Research products, page 1 of 2

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