Distributed consensus using sampled position data for second-order multi-agent systems with communication delay

Abstract

This paper investigates the distributed consensus for second-order multi-agent systems via a novel cooperative protocol which involves only sampled position data of each agent. The proposed consensus algorithm consists of two parts: a general part with communication delay and a special part with both communication and forced delays. It is revealed that the forced delay is lower bounded by a threshold and plays an important role for achieving consensus. A necessary and sufficient condition with respect to the sampling period, coupling gains, time delays, and eigenvalues of the Laplacian matrix, is established for achieving consensus under an undirected interaction topology. It is found that choosing a relatively small sampling period does not necessarily promote achieving consensus under fixed coupling gains and time delays. Finally, some illustrative examples are provided to demonstrate the effectiveness of the theoretical findings.