Local-asymptotic stability of a network congestion control system using Lyapunov-Krasovskii methods

In this paper we apply the analysis of delay differential systems to congestion control of computer networks. We derive a condition on the control gain that guarantees the stability of the network under a congestion control law using matrix equations and a Lyapunov-Krasovskii functional. We represent the congestion of the network as a set of graphs and use that structure to define a matrix equation that represents the queue dynamics of a computer network. The network model and control are based on a continuous-time fluid flow model of network traffic data rates.