Consensus Conditions of Multi-Agent Systems with Unbalanced Topology and Stochastic Disturbances

Abstract

Consensus conditions of multi-agent systems with general directed communication topology and Guassian communication noises are investigated.Here the topology includes not only the balanced graphes but also unbalanced graphes,and the latter is the main concern of this paper.By using the results of Markov chains,a communication class of network nodes is given.By considering the influence of the noises,the consensus conditions are provided:(1) for the case where the information received by some agents in the communication class corrupted by noises,a sufficient and necessary condition of mean square consensus is given.It is shown that this condition can also ensure almost sure consensus.(2) For the case where no information received by the agents in the communication class is corrupted,but the information received by some agents outside of the communication class is corrupted,a sufficient condition of mean square consensus is obtained,which is shown to be necessary in some sense.(3) For the case without noise,a sufficient and necessary condition of consensus is presented.