In this work a computational framework is proposed for the synthesis of flexible and controllable heat exchanger networks. The synthesis is projected to operate over a specified range of expected variations in the inlet temperatures and flowrates of the process streams using a decentralized control system, such that the total annual cost involving the utility consumption and the investment are optimized simultaneously. The framework is based on a two-stage strategy. A design stage is performed prior to the operability analysis where the design variables are chosen. In the second stage, the control variables are adjusted during operation on the realizations of the uncertain parameters. The framework yields a HEN design, which is guaranteed to operate with the designed control system under varying conditions ensuring stream temperature targets and optimal energy integration. The application of the proposed framework and its computational efficiency are illustrated with some numerical examples. (C) 2013 Elsevier Ltd. All rights reserved.