A new approach to consensus problems in discrete-time multiagent systems with time-delays

In this paper, consensus problems in discrete-time multiagent systems with timeinvariant delays are considered. In order to characterize the structures of communication topologies, the concept of pre-leader-fol lower decomposition is introduced. Then, a necessary and sufficient condition for state consensus is established. By this method, consensus problems in networks with a single time-delay, as well as with multiple time-delays, are studied, and some necessary and sufficient conditions for solvability of consensus problems are obtained.