A general approach to the eigenstructure assignment for reachability and stabilizability subspaces

This paper is concerned with the problem of determining basis matrices for the supremal output-nulling, reachability and stabilizability subspaces, and the simultaneous computation of the associated friends that place the assignable closed-loop eigenvalues at desired locations. Our aim is to show that the Moore-Laub algorithm in Moore and Laub (1978) for the computation of these subspaces was stated under unnecessary restrictive assumptions. We prove the same result under virtually no system-theoretic hypotheses. This provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust, and as general as the standard ones based on the computation of sequences of subspaces.