  A theorem on (partial) convergence to consensus of multiagent systems is
presented. It is proven with tools studying the convergence properties of
products of row stochastic matrices with positive diagonals which are infinite
to the left. Thus, it can be seen as a switching linear system in discrete
time. It is further shown that the result is strictly more general than results
of Moreau (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005),
although Moreau's results are formulated for generally nonlinear updating maps.
This is shown by demonstrating the existence of an appropriate switching linear
system which mimics the nonlinear updating maps. Further on, an example system
is given for which convergence to consensus can be shown by using the theorem.
In this system the lengths of intercommunication intervals in the switching
communication topology grows without bound. This makes other theorems not
applicable.
