Partial stabilisation of large-scale discrete-time linear control systems. (7th February 2006)

• Record Type: Journal Article
• Authors: Benner, Peter; Castillo, Maribel; Quintana-Orti, Enrique S.
• Is Part Of: International journal of computational science and engineering. Volume 1:Number 1(2005)
• Page Start: 15
• Page End: 21
• Publication Date: 2006-02-07
• Subjects: discrete-time linear control systems -- stabilisation -- matrix disc function -- matrix sign function -- parallel computing -- Beowulf cluster; Computer science -- Mathematics -- Periodicals; Computer simulation -- Mathematical aspects -- Periodicals; Computational intelligence -- Periodicals; 004.015105
• Languages: English
• ISSNs: 1742-7185

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.