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This paper investigates H ∞ leader-follower consensus problems of nonlinear multi-agent systems via event-triggered control. To significantly reduce the communication burdens, a distributed estimator-based event-triggered communication protocol is proposed. By using Lyapunov stability theory, matrix theory and algebraic graph theory, we derive some sufficient conditions to guarantee the leader-follower consensus with desired H ∞ performance. Distributed triggering functions are designed for three cases: fixed topologies, switching topologies with connected sub-topologies and frequently connected switching topologies. Furthermore, we prove that the Zeno-behavior can be excluded for three cases, respectively. Finally, simulations are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]