Distributed consensus for multi-agent systems with delays and noises in transmission channels

This paper studies the distributed consensus problem for linear discrete-time multi-agent systems with delays and noises in transmission channels. Due to the presence of noises and delays, existing techniques such as the lifting technique and the stochastic Lyapunov theory are no longer applicable to the analysis of consensus. In this paper, a novel technique is introduced to overcome the difficulties induced by the delays and noises. A consensus protocol with decaying gains satisfying persistence condition is adopted. Necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non-leader–follower and leader–follower cases under a fixed topology. Under dynamically switching topologies and randomly switching topologies, sufficient conditions for strong consensus and mean square consensus are also obtained. Numerical examples are given to demonstrate the effectiveness of the proposed protocols.