Stabilizing Large Control Linear Systems on Multicomputers

In this paper we present several parallel algorithms for solving the stabilization problem of control linear systems. The first stabilizing algorithm, based on Bass' method, consists of matrix computations which result difficult to parallelize. A different two-stage approach, based on highly parallel spectral division techniques, is then described and used to develop parallel algorithms for the stabilization of large linear systems. The new approach consists of two well-defined stages. First, an efficient spectral division technique is used to identify the stable part of the linear system. Then, the unstable part of the system is stabilized by means of Bass' algorithm. The experimental results on a multicomputer show considerable performance improvements of these two-stage approaches over Bass' algorithm.

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