Exponential Convergence of the Consensus Algorithm over a Shared Broadcast Channel

This article presents a particular class of consensus algorithms for multi-agent systems of continuous-time single integrators communicating over a shared broadcast channel. To deal with the problem of interference and packet collision, we consider a time-division multiple access (TDMA) protocol represented by a switching topology where only one agent can transmit at a time. A Lyapunov function is proposed to prove the exponential convergence of this class of consensus algorithms under mild assumptions. We also provide an explicit bound for the consensus errors that depends on the communication protocol parameters.