Consensus strategy for a class of multi-agents with discrete second-order dynamics

This paper investigates consensus strategies for a group of agents with discrete second-order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time-varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results.