Second-order consensus of discrete-time multi-agent systems via one-step delayed data

This paper considers the second-order consensus problem of discrete-time multi-agent systems over fixed and undirected network topologies. A distributed consensus protocol utilizing the current and one-step delayed position information is proposed. It is interesting to found that second-order consensus in such a discrete-time multi-agent system cannot be ensured without any one-step delayed position data while it can be reached by appropriately choosing the sampling interval and the coupling strength with one-step delayed position data. A necessary and sufficient condition for reaching second-order consensus in a discrete-time multi-agent dynamical system on the sampling interval, the control gain parameters and the eigenvalues of the Laplacian matrix has been established under fixed and undirected topology. Finally, numerical examples are given to illustrate the theoretical analysis.