Asynchronous Consensus of Multiple Double-Integrator Agents With Arbitrary Sampling Intervals and Communication Delays

This paper addresses asynchronous consensus problems of multiple double-integrator agents with discontinuous information transmission, where each agent receives its neighbors´ state information at discrete instants determined by its own clock. A novel consensus protocol is proposed based on continuous information of each agent itself and sampled information of each agent´s neighbors. By using nonnegative matrix theory and graph theory, we prove that the consensus problem is solvable in the asynchronous sampled-data setting without or with time-varying communication delays, if the union of the effective communication topology across any time interval with some given length contains a spanning tree. Remarkably, the sampling intervals and communication delays are allowed to be arbitrarily large yet bounded. By proposing a modified protocol based on the idea of pinning control, we extend the existing result to the desired consensus problem. Numerical examples are finally provided to validate the theoretical results.