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In this paper, we aim at developing a new approach to the design of the rate controller proposed by Chong et al. in  for the cases of both identical and heterogeneous round-trip delays in ATM networks. The design method is described by linear matrix inequalities (LMI), which can be solved efficiently by LMI toolbox in Matlab. The approach developed in this paper theoretically guarantees that the target queue length can be maintained stable for all the cases: i) where the distance between the source and the bottlenecked router is less than the maximal distance which is chosen when designing the controller parameter; and ii) where the round trip delays (RTDs) are queue-length-dependent and hence time-varying if the whole RTD is less than a given bound chosen in the design stage. The latter property is very useful in the network planning stage.