Cluster lag Consensus for Single Integrator and Double Integrator Multi-Agent Systems With a Leader of Nonzero Input

In this paper, cluster lag consensus is studied for both single integrator and double integrator MASs, respectively. The leader in both MASs has nonzero control input, which is unknown to all followers. To deal with effects caused by leader’s unknown control input, a sign function is introduced and then non-smooth protocols utilizing relative information between follower and its neighbours are proposed for single integrator and double integrator MASs, respectively. By employing appropriate Lyapunov functions and stability analysis methods, sufficient conditions for achieving cluster lag consensus are given under proposed protocols. Finally, some numerical examples are provided to illustrate the theoretical results.