A Sufficient Condition for Convergence of Sampled-Data Consensus for Double-Integrator Dynamics With Nonuniform and Time-Varying Communication Delays

This technical note investigates a discrete-time second-order consensus algorithm for networks of agents with nonuniform and time-varying communication delays under dynamically changing communication topologies in a sampled-data setting. Some new proof techniques are proposed to perform the convergence analysis. It is finally shown that under certain assumptions upon the velocity damping gain and the sampling period, consensus is achieved for arbitrary bounded time-varying communication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough.