Robust stability analysis of Smith predictor-based congestion control algorithms for computer networks

Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has been also shown that the today running TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyze the robust stability of the closed-loop system in the face of delay uncertainties that in data networks are present due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty.