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This paper investigates the design of an observer-based controller to overcome the congestion problem in the TCP/IP networks where the available link bandwidth is modeled as a time-variant disturbance. Then, a detailed description is discussed to establish a linearized mathematical model in order to ensure the robust stability of the saturated delayed system and satisfy the performance. Based on a Lyapunov–Krasovskii (L–K) functional, a generalized sector condition, and the Finsler’s Lemma, the proposed new design methodology leads to a quite simple LMI condition that is numerically tractable with any convex optimization algorithm. An effective iterative optimization algorithm is adopted to estimate the largest possible region of initial conditions as will be seen in the numerical examples where the results are compared to PI, RED, and REM controllers.