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In this paper, a novel integral sliding mode control strategy is designed for rate-based flow control problem in asynchronous transfer mode (ATM) networks. The control scheme, which includes a predictor, guarantees stability robustness to multiple time-delays in different channels and changeful available bit-rate (ABR) bandwidth. It also achieves two expectant goals, i.e. it ensures exponential convergence of queue length to the desired steady-state value and satisfies a weighted fairness condition. The algorithm exhibits good performance and most importantly, has a solid theoretical foundation. Simulation results show that the control system is rapid, robust and adaptive.