Impulsive consensus for second-order multi-agent systems with directed topology and communication time-delays

This paper focuses on the consensus problem for second-order multi-agent systems with impulsive algorithm and communication time-delays. By introducing a state transformation, the consensus of the system is translated into the asymptotical stability of a reduced-order discrete-time system. Based on the properties of Laplacian matrix of graphs and a given invertible matrix, necessary and sufficient conditions are established for the consensus convergence in the cases of directed and undirected topologies. Two numerical simulations are worked out to illustrate the effectiveness of the theoretical results.