Second-Order Multi-Agent Consensus via Delayed Relative Displacement Feedback

In this paper, a second-order multi-agent consensus via relative displacement feedback is studied. It is assumed that the velocity measurements of the agents are not available and that the position information processing is affected by a uniform bounded delay. A sufficient condition for consensus in undirected and connected topologies is provided in terms of a complex stability region for the eigenvalues of the Laplacian matrix. Moreover, a method for the evaluation of the critical delay is presented. Numerical examples illustrate the effect of the delay in different topologies.