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

In this paper, consensus problems for discrete-time multiagent systems with time-delays are considered. First, a necessary and sufficient condition for a system to solve a consensus problem is established by a new approach: pre-leaders-followers decomposition. Furthermore, by this method, consensus problems for systems with a single time-delay as well as with multiple time-delays are studied, and some necessary and sufficient conditions are established. Finally, the case with switching topologies and the case with time-varying delays are also investigated.