Multiple agents sporadically exchange data over a broadcast network according to an event-based protocol to observe and control a dynamic process. The synthesis problem of each agent's state estimator and event generator, which decides whether information is broadcast or not, is addressed in this paper. In particular, a previously proposed LMI-synthesis procedure guaranteeing closed-loop stability is extended to incorporate an ℋ₂ performance measure. The improved estimation performance of the extended design is illustrated in simulations of an inverted pendulum, which is stabilized by two agents.