Computation of the subspaces for entire eigenstructure assignment via the singular value decomposition

This short paper examines use of the singular value decomposition of the augmented matrix [A - ??I,B] to find its null space and then, subsequently, the subspace of possible closed loop eigenvectors and the necessary feedback matrix, K, for the assignment of the specified closed loop eigenvalues and eigenvectors. This paper describes the very attractive computational alternative of using the singular value decomposition rather than the previously reported approach of elementary column operations. The assignment of complex eigenvalues and repeated eigenvalues using the same basic singular value decomposition of a real matrix is also discussed.