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This paper describes a novel multi-rate multicast congestion control scheme based on the well-known proportional plus integrative control technique, where the control parameters can be designed to ensure the stability of the control loop In terms of source rate. The congestion controller is located at the next upstream nodes of multicast receivers and has explicit rate (ER) algorithm to regulate the rate of the receivers. We further analyze the theoretical aspects of the proposed algorithm, show how the control mechanism can be used to design a controller to support many-to-many multi-rate multicast transmission based on ER feedback, and verify its agreement with simulations in the case of bottleneck link appearing in a multicast tree. Simulation results show the efficiency of our scheme in terms of the system stability, high link utilizations, fast response, scalability, high throughput and fairness.