Fundamental, reachability, and observability matrices for discrete descriptor systems

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 are defined. It is shown that the natural space for analyzing descriptor system properties is
R^{2n}
(where
n
is the dimension of the system), not R
ⁿ
as is the case for state-space systems. Solutions are provided for the descriptor open-loop control and estimation problems.