A convergence result for multiagent systems subject to noise

We present conditions under which a general class of multiagent systems subject to noise can reach agreement in expected value with probability one. The noise can be induced by the fact that each agent takes erroneous measurements of neighbors´ positions. The class of systems considered may be nonlinear and requires that the diameter of the agents be bounded for all possible error measurements. The convergence result is related to previous work on the robustness of the rendezvous algorithm and the stability of multiagent systems with periodic connectivity. We illustrate the results in terms of a modified discrete-time Kuramoto system, which is amended to guarantee the system requirements.