Distributed tracking of second-order multi-agent systems with measurement noise

This paper is concerned with the leader-following consensus problem of second-order agents under fixed and directed topologies. The control input of each agent can only use its local state and the states of its neighbors corrupted by white noises. By using Hurwitz stability criteria, Ito formula and graph theory, some necessary and sufficient conditions are given for mean square bounded tracking. Furthermore, if the leader's acceleration has a limit when the time goes to infinity, we give an explicit expression of the tracking error in relation to the network and control parameters. Finally, the effectiveness of the distributed tracking controller is demonstrated by a simulation example.