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A unified framework for the numerical solution of general quadratic matrix equations |
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| Authors: | Tsachouridis Vassilios A; Karcanias Nicos; Postlethwaite Ian |
| Institution: | 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 |
| Abstract: | ** Email: vassilios.tsachouridis{at}ieee.org*** Email: N.karcanias{at}city.ac.uk**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature. |
| Keywords: | numerical algorithms homotopy methods matrix equations Riccati equations control systems |
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