Leaderless coordination via bidirectional and unidirectional time-dependent communication

We study a simple but compelling model of n interacting agents with time-dependent, bidirectional and unidirectional communication. The model finds wide application in a variety of fields including swarming, synchronization and distributed decision making. In the model, each agent updates his current state based upon the current information received from other agents according to a simple weighted average rule. Necessary and/or sufficient conditions for the convergence of the individual agents' states to a common value are presented, extending recent results reported in the literature. Further, it is observed that more communication does not necessarily lead to better convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.