Abstract
This work focuses on the leader-following consensus problem for networks of dynamic agents, each of which has second-order nonlinear time-delayed dynamics. Event-triggered control and pinning control strategies are used in view of energy conservation. For each agent, the controller updates only when a properly presented event triggering condition is satisfied, which is based on the measurement errors and an exponential term. The network communication topology contains a directed spanning tree and only a fraction of follower agents can obtain the leader agent's information. By virtue of the Lyapunov-Krasovskii functional method, the M-matrix theory and some algebraic inequalities, a sufficient condition for achieving leader-following consensus is established. The Zeno-behavior of triggered time sequence is excluded whether the consensus is reached or not. Finally, a simulation example is provided to demonstrate the proposed theoretical results.