Consensus tracking control of multi-agent systems with an active virtual leader: time delay case

This paper studies the consensus tracking issue of second-order multi-agent systems with an active virtual leader and time delays. We aim to seek the upper bound of time delay τ^* such that the multi-agent systems can achieve the consensus tracking for τ ∈ [0, τ^*). Different methods such as Lyapunov-Razumikhin theory, Hopf bifurcation theory and matrix analysis method are employed to establish the corresponding consensus tracking criteria for continuous-time and discrete-time multi-agent systems, respectively. Finally, numerical examples are given to show the effectiveness of our theoretical results.