Zero-controllability and dead-beat control of discrete-time behaviors

In this paper the concepts of controllability and zero-controllability of a (to be controlled) variable w through a (control) variable c are introduced and characterized. By assuming this perspective, the dead-beat control (DBC) problem is posed as the problem of designing a controller such that, for the resulting controlled behavior, the to be controlled variable w goes to zero in a finite number of steps in every trajectory. Zero-controllability of w through c turns out to be a necessary and sufficient condition for the existence of “admissible” DBC's.