Journal Article

A unified framework for the numerical solution of general quadratic matrix equations

Vassilios A. Tsachouridis, Nicos Karcanias and Ian Postlethwaite

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 2, pages 259-287
Published in print June 2007 | ISSN: 0265-0754
Published online June 2007 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnl023
A unified framework for the numerical solution of general quadratic matrix equations

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Algebraic quadratic equations are special cases of a single generalized algebraic quadratic matrix equation (GQME). This paper focuses on the numerical solution of the GQME using probability-1 homotopy methods. A synoptic review of these methods and their application to algebraic matrix equations is provided as background. A large variety of analysis and design problems in systems and control are reported as special cases of the presented framework and some of them are illustrated via numerical examples from the literature.

Keywords: numerical algorithms; homotopy methods; matrix equations; Riccati equations; control systems

Journal Article.  0 words. 

Subjects: Mathematics

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