This paper considers the distributed model predictive control (DMPC) of systems with interacting subsystems having decoupled dynamics and constraints but coupled costs An easily-verifiable constraint is introduced to ensure asymptotic stability of the overall system in the absence of disturbance The constraint introduced has a parameter which allows for the performance of the DMPC system to approach that controlled by a centralized model predictive controller When the subsystems are linear and additive disturbance is present the added constraint ensures the state of each subsystem converges to its respective minimal disturbance invariant set The approach is demonstrated via several numerical examples (C) 2010 Elsevier Ltd All rights reserved