Subspace recursions and structure algorithms for singular systems

We define the output-nulling (ON) (A,E,B)-invariant subspaces for singular systems, showing their dynamic significance. A Generalized Lyapunov equation is introduced to compute such a subspace, the feedback required to assign it as a closed-loop invariant subspace, and also the spectrum assigned by that feedback on the subspace. A definition of teachability subspace for singular systems is given. A new singular system structure algorithm is related to the supremal ON (A,E,B)- invariant subspace.