Partial stabilization of large-scale discrete-time linear control systems

Abstract

We propose a parallel algorithm for stabilizing 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 stabilizing 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.