Robust Control Problem as H 2 and H ∞ control problem applied to the robust controller design of Active Queue Management routers for Internet Protocol

During the last years, the Internet Application (Remote Flexible Control and Instrumentation, Telecontrol...) has retained the attention of Control researchers for modeling and studying the congestion control of TCP/IP (Transfer Control Protocol/Internet Protocol) networks. The controllers proposed in the literature such as RED (Random Early Detection) or PID (Proportional Integrate Derivative) or H2/H∞ (H2 norm/H infinity norm), give good performance under certain conditions, but they become unstable if the input delay or/and the parameters of the networks change beyond some limits. Different papers have treated the H2/H∞ robust control problem, but in this paper, adding to formulate and solve the standard robust control problem as an H2/H∞, and synthesize corresponding controllers H2, H∞ and mixed sensitivity controller, we will show how the Routh –Hurwitz criterion is weak in front of the small gain theorem, and does not guarantee the robustness of the system. Keywords— AQM, controller, fragility, H2, H∞, Robust Control, Routh-Hurwitz, sensitivity, TCP.