Second-Order Consensus of Leader-Following Multi-Agent Systems with Jointly Connected Topologies and Time-Varying Delays

In this paper, we discuss, respectively, second-order leader-following consensus problems with and without time-varying communication delays. Lyapunov theorems and matrix approach are employed to prove that all the leader-following agents will achieve second-order consensus if the velocity communication topology between the leader and each following agent is connected and the position communication topologies of all the leader-following agents are jointly connected. Several simulation results are presented to support the effectiveness of our theoretical results.