  This work proposes a new mathematical model for the TCP/AQM system that aims
to improve the accuracy of existing fluid models, especially with respect to
the sequential events that occur in the network. The analysis is based on the
consideration of two time bases, one at the queue's router level and the other
at the congestion window level, which leads to the derivation of a new
nonlinear two-dimensional fluid model for Internet congestion control. To avoid
the difficult task of assessing stability of a 2D nonlinear dynamic model, we
perform a local stability analysis of a 2D linear TCP AQM model. By
constructing a new two dimensional second order Bessel Legendre Lyapunov
functional, new matrix inequalities are derived to evaluate the stability of
the 0-input system and to synthesize a feedback controller. Finally, two
Internet traffic scenarios, with state space matrices for replicability, are
presented, demonstrating the validity of the theoretical results.
