An approach to multi-rate distributed control design for process networks is presented, where the local measurements, local control and controller communication are allowed to operate at different sampling rates. Dissipative systems theory is used to facilitate stability and performance analysis of the process network, based upon dynamic supply rates which have been lifted into a global sampling rate. Quadratic difference forms are used as supply rates and storage functions, leading to less conservative stability and performance conditions as compared to classical types of supply rates. These theoretical results are illustrated by a case study of a heat exchanger network. (C) 2014 Elsevier Ltd. All rights reserved.