In this paper, we aim at developing an H-infinity approach to the design of an active queue management (AQM) based congestion controller for the Internet Protocol. In the approach, the available link bandwidth is modelled as a nominal constant value, which is known to the link, plus a time-variant disturbance, which is unknown. The design objective is to minimize the ratio, denoted as gamma, between the norm of the perturbed queue length and that of the disturbance. An important feature of the approach is that the system performances, including the disturbance rejection ratio gamma and hence the stability of closed-loop systems, are guaranteed for all round-trip times that are less than a known value. The design is described by matrix inequalities, which can be efficiently solved by the linear matrix inequality toolbox in Matlab. (C) 2008 Elsevier Ltd. All rights reserved.