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A fundamental and required property of congestion control algorithms in computer networks is stability. In this study, a class of appropriate Lyapunov functionals is proposed to investigate asymptotic stability in the second-order congestion control systems with heterogeneous communication delays. Novel linear matrix inequality-based delay-dependent stability criteria are given by exploiting free weighting matrices, which can overcome conservativeness of most methods involving a fixed model transformation. Simulation results show that the stability criteria proposed in this study are less conservative in the sense that larger range of control gains and communication delays can be accommodated.