Geometric structure and feedback in singular systems

The output-nulling (A, E, R(B))-invariant subspaces are defined for singular systems, rigorously justifying the name and demonstrating that special cases of these geometric objects are the familiar subspace of admissible conditions and the supremal (A, E, R(B ))-invariant subspace. A novel singular-system-structure algorithm is used to compute them by numerically efficient means. Their importance for describing the possible closed-loop geometric structure in terms of the open-loop geometric structure is shown. An approach to spectrum assignment in singular systems that is based on a generalized Lyapunov equation is introduced. The equation is used to compute feedback gains to place poles and assign various closed-loop invariant subspaces while guaranteeing closed-loop regularity