Discrete-time average-consensus under switching network topologies

This paper develops a distributed algorithm for average-consensus in a discrete-time framework based on a formal matrix limit definition of average-consensus. Using this algorithm, the average-consensus problem is solved under switching network topologies provided that the network switch between instantaneously balanced, connected-over-time networks. In other words, if at each instant the network is balanced and the union of graphs over every interval T is connected, then average-consensus can be achieved. An interesting product of this analysis is the notion of "deadbeat" consensus where a system of agents achieves consensus (average or otherwise) in finite time rather than asymptotically