-This paper extends recent results by Garcia et al. on event-triggered communication to reach consensus in multi-agent systems. First, it studies the effect of two types of additive and bounded state perturbations on the consensus and on the communications. Second, it describes an improved agent state estimator as well as an estimator of the state estimation uncertainty to trigger communications. Convergence to consensus is studied. Simulations show the effectiveness of the proposed estimators in presence of state perturbations.