This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time networks. The conditions are derived by means of vector Lyapunov functions.

The obtained results are applied to traffic networks for the derivation of sufficient conditions for global exponential stability of the uncongested equilibrium point of the network. Specific results and algorithms are provided for freeway traffic models. Various examples illustrate the applicability of the obtained results.