A decentralized controller that uses event-triggered communication scheduling is developed for the leader-follower consensus problem under fixed and switching communication topologies. To eliminate continuous interagent communication, state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors. The communication times are based on an event-triggered approach and are adapted based on the trade-off between the control system performance and the desire to minimize the amount of communication. An important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed. Since the control strategy produces switched dynamics, analysis is provided to show that Zeno behavior is avoided by developing a positive constant lower bound on the minimum inter-event interval. A Lyapunov-based convergence analysis is also provided to indicate bounded convergence of the developed control methodology.