Decentralised rate-based flow controller design in multi-bottleneck data-communication networks is considered. An H∞ problem is formulated to find decentralised controllers which can be implemented locally at the bottleneck nodes. A suboptimal solution to this problem is found and the implementation of the decentralised controllers is presented. The controllers are robust to time-varying uncertain multiple time-delays in different channels. They also satisfy tracking and weighted fairness requirements. Lower bounds on the actual stability margins are derived and their relation to the design parameters is analysed. A number of simulations are also included to illustrate the time-domain performance of the proposed controllers.