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IMA Journal of Mathematical Control and Information Advance Access originally published online on August 7, 2006
IMA Journal of Mathematical Control and Information 2007 24(2):259-287; doi:10.1093/imamci/dnl023
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Vassilios A. Tsachouridis**,1, Nicos Karcanias***,1 and Ian Postlethwaite****,2

1 School of Engineering and Mathematical Sciences, City University London, Northampton Square, London EC1V 0HB, UK, 2 Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK

** Email: vassilios.tsachouridis{at}ieee.org

*** Email: N.karcanias{at}city.ac.uk

**** Email: ixp{at}le.ac.uk


  Abstract

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.


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