Consensus of second-order multi-agent systems under communication delay

In this paper, the leader-following consensus problem is investigated for the second-order multi-agent systems with communication delay. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions, consensus conditions in the form of linear matrix inequality (LMI) are obtained for the system with time-varying communication delays and static interconnection topology converging to the leader's states respectively. In addition, by constructing Lyapunov-Krasovskii functional, delay-dependent consensus condition in the form of LMI is also obtained for the system with time-invariant communication delay and switching topology. Simulation results illustrate the correctness of the results.