Consensus of second-order multi-agent systems with a time-varying reference signal via sampled control

For second-order multi-agent systems with both a time-varying reference velocity signal, and time-varying reference position and velocity signals, respectively, this paper studies the corresponding consensus issue in a sampling setting under directed communicated topology. Firstly, necessary and sufficient consensus criteria are established for both cases. Moreover, whether the communicated topology graph has a directed spanning tree has nothing to do with the consensus of multi-agent system with time-varying position and velocity reference signals. Then we further extend the results to the complicated case where the Cartesian coordinate coupling is introduced and give the specific size of Euler angle of the rotation matrix. Finally, numerical examples are given to show the effectiveness of our results.