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The bursty events of available bit rate (ABR) traffic challenge the research on flow control algorithm. This bursty nature makes the network difficult to guarantee some performance such as decreasing cell loss especially when congestion appears. In addition the robust stability analysis in the presence of virtual connections (VCs) variation is another inherent problem of the current rate-based algorithm. An explicit rate-based scheme is concerned. Some mathematical methods are adopted to minimize overshoot in the buffer to eliminate the growing congestion quickly. Then in linear matrix inequality (LMI) forms via Lyapunov stability argument relating to robustness issues in the presence of time-varying VCs is purposed in linear matrix inequality. A set of numerical examples guarantees this choice of algorithm parameters is robust stability. The simulations further back up our results.