Dead-beat estimation problems for 2D behaviors on Z+ × Z

In this paper, dead-beat estimation problems for a class of two-dimensional (2D) discrete behaviors, defined on the grid Z+ × Z and having the time as (first) independent variable, are investigated. For this class of behaviors, the concepts of observability and reconstructibility are defined and fully characterized. The dead-beat observer (DBO) problems and parametrization of all dead-beat observers are introduced and solved. Finally, the general dead-beat estimation theory are obtained and are applied to deal with 2D state space model.