Results are developed to ensure stability of a dissipative distributed model predictive controller in the case of structured or arbitrary failure of the controller communication network; bounded errors in the communication may similarly be handled. Stability and minimum performance of the process network is ensured by placing a dissipative trajectory constraint on each controller. This allows for the interaction effects between units to be captured in the dissipativity properties of each process, and thus, accounted for by choosing suitable dissipativity constraints for each controller. This approach is enabled by the use of quadratic difference forms as supply rates, which capture detailed dynamic system information. A case study is presented to illustrate the results. (c) 2014 American Institute of Chemical Engineers AIChE J, 60: 1682-1699, 2014