Descriptor systems: Fundamental matrix, reachability and observability matrices, subspaces

This paper uses the fundamental matrix of a regular discrete descriptor system to derive expressions for descriptor reachability and observability matrices. Reachable and unobservable subspaces and a subspace of admissible boundary conditions are defined. It is shown that the natural space for analyzing descriptor system properties seems to be R2n (where n is the dimension of the system), not Rn as is the case for state-space systems. Solutions are provided for the descriptor open-loop control and estimation problems.