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Explicit direct solution of the Lyapunov matrix equation

โœ Scribed by Z. Jacyno

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
497 KB
Volume
326
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

A new method of explicit direct solution for the Lyapunov matrix equation is proposed. Based on a fundamental property allowing the decomposition of any arbitrary matrix into symmetric and skew-symmetric parts, the Lyapunov matrix is expressed in a simple and compact form. In addition, a sign$cant reduction in the size of the algebraic computational problem is achieved. The number of algebraic linear equations to be solved is reduced by the order of magnitude equal to the dimension of a considered system. A few examples comparing the proposed method with a direct solution of the Lyapunov equation are given.

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Comments on โ€œExplicit direct solution of
Comments on โ€œExplicit direct solution of the Lyapunov matrix equationโ€
โœ A.L. Zelentsovsky ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 119 KB

Comments und Rebuttal advantage indicated. He is quoting to this effect reference (3). This paper deals, though, with discrete systems and the Lyapunov equation of the type shown in'its title, while our paper (4) concerns continuous systems. Such systems are mentioned in (3) in a brief remark only,