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.