Consensus of a leader-following multi-agent system with negative weights and noises

This study is concerned with the issue of mean-square consensus for a model of leader-following multi-agent system. The agents acting as followers update states based on the information received from the time varying neighbours and the virtual leader. Negative weights besides positive weights are introduced for the links existing among the agents. Moreover, all followers considered here are influenced by noises with different intensities emerging from the external environment or transmission channels. In order to guarantee consensus of the multi-agent system under the noises, the corresponding sufficient conditions are derived. Theoretical proofs are given mainly by using the Lyapunov function approach and the stochastic analysis. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.