Dead beat observer synthesis

In the paper the observer design problem is investigated in the context of linear left shift invariant discrete behaviors, whose trajectories have support on the positive axis. Observability and reconstructibility properties of certain manifest variables from certain others, in the presence of latent variables, are defined and fully characterized. Necessary and sufficient conditions for the existence of either a dead-beat or an exact observer are introduced, and a complete parametrization of all dead-beat observers is given.