Leader-following consensus for linear multi-agent systems with measurement noises

This paper investigates a leader-following consensus problem for high-order linear multi-agent systems under a directed graph topology, containing a spanning tree. It is supposed that each agent can obtain full state of itself and receive its neighbors' state with noises, where the intensities of noises are vector functions of relative states of agents. To achieve leader-following consensus in this scene, a consensus protocol is designed, where the gain matrix is obtained by the algebraic Riccati equation and the coupling strength should be restricted in a given interval. Specifically, the lower bound of the interval ensures the consensus and the upper bound of the interval is devoted to limit the effects of noises, then the designed protocol could attenuate the noises while driving the multi-agent systems to consensus. Finally, a simulation example is given to show the correctness of the proposed results.