A set-membership approach to consensus problems with bounded measurement errors

This paper analyzes two classes of consensus algorithms in presence of bounded measurement errors. The protocols taken into account adopt an updating rule based either on constant or vanishing weights. The bounded error assumption allows one to cast the consensus problem in a set-membership framework, and to study the team agreement in terms of the evolution of the feasible state set. It is shown that consensus cannot be guaranteed with respect to all possible noise realizations. Moreover, bounds on the asymptotic difference between the states of the agents are explicitly derived, in terms of the bounds on the measurement noise and the eigenvalues of the weight matrix.