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Motivated by the limitations of current optimal flow control approach, we develop a new utility max-min flow control framework using classic sliding mode control. It consists of a source algorithm and a binary congestion feedback mechanism, in which only the sources with the highest utility at each congested link are required to reduce their transmission rates. It can be directly applied to a multi-service network with heterogeneous applications that have different QoS characteristics. The proposed framework achieves the utility max-min fairness among applications efficiently in the sense of low overhead and rapid convergence. Rigorously, the system is proven to be asymptotically stable by means of Lyapunov's theorem.