Equivalent conditions for uniform asymptotic consensus among distributed agents

A set of conditions equivalent to uniform asymptotic consensus for distributed agents involving switched stability theory, linear matrix inequalities, and graph-theoretic notions has been established. These conditions are presented for both leaderless and leader-follower situations and extend previous results to wider classes of multi-agent systems. In particular, the uniformity requirement imposed on the convergence rate of mixed matrix products not only plays a crucial role in theoretical developments, but it also meets the practical needs of reaching consensus robustly against disturbances.