Leader-following consensus of second-order multi-agent systems with time-delay and nonlinear dynamics

This paper concern a leader-following consensus problem of a second-order multi-agent system with time-delay. The state of the considered leader not only the position and velocity keeps changing but also with time-delay and nonlinear dynamics. To track such a leader, neighbor-based distribute controller is given for each autonomous. Based on Lyapunov-Razumikhin functions, some sufficient conditions are obtained for reaching second-order leader-following consensus with nonlinear dynamics. In addition, the consensus problems that the leader and each agent without nonlinear dynamics are discussed, and get some sufficient conditions which render the system reach consensus. Finally, the simulation examples illustrate the obtained theory results.