The parallel structure is one of the basic system architectures found in process networks. In order to achieve robust control of complex process networks, it is necessary to formulate control strategies that specifically accommodate the characteristics of such parallel systems. In this paper, the competitive coupling and competitive constraints in parallel systems are initially defined. A novel robust distributed model predictive control algorithm is then developed for such parallel systems which deals explicitly with competitive couplings, competitive constraints and uncertainties. The Lyapunov Method is used for the theoretical analysis which produces tractable linear matrix inequalities (LMI). Two simulation studies and an experimental trial are provided to validate the effectiveness of the proposed approach. These consider control of 40 user and 100 user gas boiler heating systems as well as control of two continuous stirred tank reactors (CSTRs) which are connected in parallel. (C) 2019 Elsevier Ltd. All rights reserved.