This thesis uses a modern control approach to address the Internet traffic control issues in the Transport Layer. Through literature review, we are interested in using the H2/H∞ formulation to obtain the good transient performance of an H2 controller and the good robust property from an H∞ controller while avoiding their deficiencies. The H2/H∞ controller is designed by formulating an optimization problem using the H2-norm and the H∞-norm of the system, which can be solved by an LMI approach using MATLAB. Our design starts with the modeling of a router and the control system by augmenting the network plant function with the Sensitivity function S, the Complementary Sensitivity function T and the Input Sensitivity function U. These sensitivity functions along with their weight functions are used to monitor the closed-loop dynamics of the traffic control. By choosing different combinations of the sensitivity functions, we can obtain the SU, the ST and the STU controllers. Both the window-based and rate-based version of these different types of H2/H∞ controllers have been designed and investigated. We have also proved that these controllers are stable using Lyapunov’s First Method. Next, we verify the performance of the controllers by OPNET simulation using different performance measures of queue length, throughput, queueing delay, packet loss rate and goodput. Our performance evaluation via simulation has demonstrated the robustness and the better transient response such as the rise/fall time and the peak queue value. We have also investigated the controller performances subject to network dynamics as well as through comparison with other controllers. Finally, we have improved these controllers for real-time application. They are capable to update/renew the controller in a short time whenever new network parameter values are detected so that the optimum performance can be maintained.