Consensus protocols for discrete-time multi-agent systems with time-varying delays

This paper addresses consensus problems for discrete-time multi-agent systems with time-varying delays and switching interaction topologies and provides a class of effective consensus protocols that are built on repeatedly using the same state information at two time-steps. We show that those protocols can solve consensus problems under milder conditions than the popular consensus algorithm proposed by Jadbabaie et al., specifically, the presented protocols allow for the case that agents can only use delayed information of themselves, whereas the popular one is invalid. It is proved that if the union of the interaction topologies across the time interval with some given length always has a spanning tree, then in the presence of bounded time-varying delays, those protocols solve consensus problems.