On the general consensus protocol in multi‐agent networks with second‐order dynamics and sampled data

This paper considers the problem of the convergence of the consensus for multiple agents in a directed network. A general distributed consensus protocol is designed, the advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. Necessary and sufficient conditions are established for reaching consensus of the system by choosing the appropriate sampling period, the control parameters and the spectra of the Laplacian matrix. It is found that second‐order consensus cannot be reached for a sufficiently large sampling period while it can be reached for a sufficiently small one. Furthermore, the coupling gains can be carefully designed under the given network structure and the sampling period. Finally, a simulation example is given to verify and illustrate the theoretical analysis.