A further result on consensus problems of second-order multi-agent systems with directed graphs, a moving mode and multiple delays

This paper considers a consensus problem of a class of second-order multi-agent systems with a moving mode and multiple delays on directed graphs. Using local information, a distributed algorithm is adopted to make all agents reach a consensus while moving together with a constant velocity in the presence of delays. To study the effects of the coexistence of the moving mode and delays on the consensus convergence, a frequency domain approach is employed through analyzing the relationship between the components of the eigenvector associated with the eigenvalue on imaginary axis. Then based on the continuity of the system function, an upper bound for the delays is given to ensure the consensus convergence of the system. A numerical example is included to illustrate the obtained theoretical results.