A Global Detectability Condition for Consensus Tracking of Linear Multi-Agent Systems with StochasticDisturbances

This paper investigates the consensus tracking problem for both continuous- and discrete-time multi-agent systems with general linear dynamics and stochastic disturbances under a global detectability condition. It is assumed that there exists a dynamic leader and the subgraph describing the communication topology among the followers is undirected and connected. The proposed global detectability condition extends the traditional local detectability condition to the networked case. By using the relative states of neighboring followers and the relative measurement information of the leader, distributed observer-type consensus protocols are constructed for both continuous- and discrete-time cases to guarantee all the followers to track the leader. A distinct feature of this paper is that the relative states of the leader are estimated by a group of followers rather than any individual follower. It is found that the mean square tracking errors are bounded even if the leader is not detectable by any follower, where the only requirement is that the leader is globally detectable by followers. Simulation results are finally presented to verify the effectiveness of theoretical results.National Natural Science Foundation of China [61225013, 61304168, 11332001]; Natural Science Foundation of Jiangsu Province of China [BK20130595]SCI(E)EIARTICLEduanzs@pku.edu.cn1,SI357-3661