Partial stabilisation of large-scale discrete-time linear control systems. (7th February 2006) - Benner, Peter; Castillo, Maribel; Quintana-Orti, Enrique S.
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.