Partial interconnection dead-beat control of two-dimensional behaviors

In this paper the dead-beat control problem, by partial interconnection, of two-dimensional discrete behaviors, defined on the grid ℤ₊ × ℤ and having the time as (first) independent variable, is investigated. It turns out that the possibility of driving to zero (in a finite number of “steps”) the “relevant variables” by means of a partial interconnection controller, making use of the “measurable variables”, is equivalent to the reconstructibility of the relevant variables, that are not accessible for control. On the other hand, if we search for “admissible” dead-beat controllers, the only ones that provide meaningful results in practice, an additional condition has to be introduced: the zero-time-controllability of the relevant variables.