In this letter, we investigate the local stability in equilibrium for Internet congestion control algorithm proposed by Low (IEEE/ACMTRANSACTIONS ONNETWORKING, 1999). The network consists of multisource and one-bottleneck link with heterogenous time-varying propagation delays. Linear matrix inequality (LMI) stability criteria is presented for discrete congestion control algorithm of TCP/REM dual model, which can be efficiently and easily solved by the LMI toolbox provided by Matlab software. An important feature is to acquire the maximum network delays to guarantee the stability of congestion control algorithm, i.e., the scale stability domain of REM algorithm. Index Terms-Congestion control, linear matrix inequality (LMI), Local stability, REM.