Efficient parallel algorithms for controllability and eigenvalue assignment problems

The design and analysis of time-invariant linear control systems give rise to a variety of interesting linear algebra problems. Numerically viable sequential algorithms now exist for most of these problems; however, efficient parallel algorithms are virtually nonexistent. In this paper, we propose efficient parallel algorithms for multi-input controllability problem and the single-input pole assignment problem. A desirable feature of these algorithms is that they are composed only of basic linear algebraic operations such as vector-matrix multiplication, solution of a linar system and computation of eigenvalues or singular values of a symmetric matrix, for which efficient parallel algorithms have already been developed. Thus, the proposed algorithms have potentials for implementations on some existing and future parallel processors.