On the computation of reachability, stabilisability and output-nulling subspaces using the Rosenbrock system matrix

In this paper we offer a set of algorithms for the computation of the fundamental subspaces of linear time-invariant (LTI) systems, which appear in the solution of a large number of control and estimation problems. In particular, we employ the Rosenbrock system matrix pencil to provide algorithms for the computation of output-nulling, reachability and stabilisability subspaces. We show via an example that these methods can offer superior reliability than other commonly used methods employing subspace recursions.