Title: Partial stabilisation of large-scale discrete-time linear control systems

Authors: Peter Benner, Maribel Castillo, Enrique S. Quintana-Orti

Addresses: Fakultat fur Mathematik, Technische Universitat Chemnitz, 09107 Chemnitz, Germany. ' Depto. de Ingenieria y Ciencia de Computadores, Universidad Jaume I, 12.071–Castellon, Spain. ' Depto. de Ingenieria y Ciencia de Computadores, Universidad Jaume I, 12.071–Castellon, Spain

Abstract: We propose a parallel algorithm for stabilising large, discrete-time, linear control systems on a Beowulf cluster. Our algorithm first separates the Schur stable part of the linear control system using an inverse free iteration for the matrix disc function and then computes a stabilising feedback matrix for the unstable part. This stage requires the numerical solution of a Stein equation. This linear matrix equation is solved using the sign function method after applying a Cayley transformation to the original equation. The experimental results on a cluster composed of Intel PII processors and a Myrinet interconnection network show the parallelism and scalability of our approach.

Keywords: discrete-time linear control systems; stabilisation; matrix disc function; matrix sign function; parallel computing; Beowulf cluster.

DOI: 10.1504/IJCSE.2005.008907

International Journal of Computational Science and Engineering, 2005 Vol.1 No.1, pp.15 - 21

Published online: 02 Feb 2006 *

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