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ELA

NEW ESTIMATES FOR THE SOLUTION OF THE LYAPUNOV

MATRIX DIFFERENTIAL EQUATION

∗

JUAN ZHANG† AND JIANZHOU LIU†

Abstract. In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

Key words.Lyapunov matrix differential equation, Eigenvalue bounds, Majorization inequality.

AMS subject classifications.93D05, 15A24.

∗ Received by the editors November 30, 2009. Accepted for publication December 31, 2009.

Handling Editor: Daniel Szyld.

†Department of Mathematics and Computational Science, Xiangtan University, Xiangtan,

Hu-nan 411105, China ([email protected]). Supported in part by Natural Science Foundation of China(10971176).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 6-19, January 2010

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