  We consider continuous-time consensus seeking systems whose time-dependent
interactions are cut-balanced, in the following sense: if a group of agents
influences the remaining ones, the former group is also influenced by the
remaining ones by at least a proportional amount. Models involving symmetric
interconnections and models in which a weighted average of the agent values is
conserved are special cases. We prove that such systems always converge. We
give a sufficient condition on the evolving interaction topology for the limit
values of two agents to be the same. Conversely, we show that if our condition
is not satisfied, then these limits are generically different. These results
allow treating systems where the agent interactions are a priori unknown, e.g.,
random or determined endogenously by the agent values. We also derive
corresponding results for discrete-time systems.
