On the structure theory of discrete-time linear systems

Abstract

The paper deals with the canonical decomposition of discrete-time linear systems based on the classical properties of reachability, controllability, observability and reconstructibility. First, a set of relationships between the structural subspaces is established and used to derive a general form of the discrete-lime duality principle. By means of these results, a sufficient condition for the existence of a canonical decomposition is worked out. Such a condition is also necessary if the attention is focused on decompositions based on the classical structural properties. Depending on the pair of properties considered, four different decompositions can be achieved. Finally, by making reference to controllability and reconstructibility a canonical decomposition is shown to exist for periodic systems. In general, non-reversible periodic systems admit no other decomposition but this one.