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A modified matrix sign function method for projected Lyapunov equations

Please always quote using this URN:urn:nbn:de:0296-matheon-3443
  • In this paper we discuss the numerical solution of projected generalized Lyapunov equations using the matrix sign function method. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. It is known that the matrix sign function method applied to a matrix pencil $\lambda E-A$ converges if and only if $\lambda E-A$ is of index at most two. The convergence is quadratic if $E$ is nonsingular, and it is linear, otherwise. We will propose a modification of the matrix sign function method that converges quadratically for pencils of arbitrary index. Numerical examples will be presented to demonstrate the properties of the modified method.

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Metadaten
Author:Tatjana Stykel
URN:urn:nbn:de:0296-matheon-3443
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/06/21
Release Date:2006/06/15
Tag:
Institute:Technische Universität Berlin
Preprint Number:336
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