A Mean Square Consensus Of General Linear Multiagent Dynamics Systems With Noises

The mean square consensus of general linear multi-agent systems with noises is researched in the presence of no leader and multiple leaders in this paper. Two kinds of topologies are considered in the paper: one topology is an undirected connected topology in the case of no leader; another one is a directed topology which for each follower, there exists at least one leader that has a directed path to that follower in the case of multiple leaders. The designed distributed protocols in the two parts are composed of the relative states between agent and its neighbor agents and the agent's own state feedback. Because of the existence of noises,the agent of state measurements cannot be obtained accurately.The protocol applies a time-varying gain vector a(t)K to attenuate the noise effect. The paper gets the sufficient conditions on the mean square consensus of protocol relying on algebraic graph theory, Lyapunov control method, Riccati inequation, stochastic analysis so that the multi-agent systems realize system stability.