Consensus of second-order discrete-time multi-agent systems with fixed topology

This paper studies the consensus of second-order discrete-time multi-agent systems with fixed topology. First, we formulate the problem and give some preliminaries. Then, by algebraic graph theory and matrix theory, the convergence of system matrix is analyzed. Our main results indicate that the consensus of second-order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters satisfy a range. The eigenvalues of the corresponding Laplacian matrix play a key role in reaching consensus. Finally, numerical simulations are given to illustrate the results.