On the eigenstructure assignment of singular systems

We examine the feedback assignment of eigenstructure for linear time-invariant singular systems. The possible closed-loop structure is investigated using the reachable and supremal (A,E,R(B))-invariant subspaces. No controllability assumptions are made. It is shown how to determine in terms of the original system matrices exactly what is possible using feedback; no transformation to special form is needed. A method is given to compute the required feedback gain.