In this paper, an analytical method for the design of a congestion control scheme in packet switching networks is presented. This scheme is particularly suitable for implementation in ATM switches, for the support of the available bit rate (ABR) service in ATM networks. The control architecture is ratebased with a local feedback controller associated with each switching node. The controller itself is a generalization of the standard proportional-plus-derivative controller, with the difference that extra higher-order derivative terms are involved to accommodate the delay present in high-speed networks. It is shown that, under the specific service discipline introduced here, there exists a set of control gains that result in asymptotic stability of the linearized network model. A method for calculating these gains is given. In addition, it is shown that the resulting steady state rate allocation possesses the so-called max-min fairness property. The theoretical results are illustrated by a simulation example, where it is shown that the controller designed, using the methods developed here, works well for both the service discipline introduced in this paper and for the standard FCFS scheme.