  This paper studies a fundamental relation that exists between stabilizability
assumptions usually employed in distributed model predictive control
implementations, and the corresponding notions of invariance implicit in such
controllers. The relation is made explicit in the form of a theorem that
presents sufficient conditions for global stabilizability. It is shown that
constraint admissibility of local robust controllers is sufficient for the
global closed-loop system to be stable, and how these controllers are related
to more complex forms of control such as tube-based distributed model
predictive control implementations.
