Existence of Reachable and Observable Triples of Linear Discrete-Time Descriptor Systems

This work studies the reachability and observability of discrete-time descriptor systems and considers the following problem: Given a matrix pair (E, A), find a matrix B (C) such that the corresponding descriptor system is not reachable (observable). The computation of such a matrix can give us a set of conditions that can then be taken into account when constructing the matrix B (C) to make the system reachable (observable). The above problem is solved by working on the equivalent causal and noncausal subsystems that are obtained through the Weierstrass decomposition of discrete-time descriptor systems. Positive descriptor systems are also considered. The developed theory is illustrated through physical and numerical examples.