Convergence of sampled-data consensus algorithms for double-integrator dynamics

This paper studies convergence of two consensus algorithms for double-integrator dynamics with intermittent interaction in a sampled-data setting. The first algorithm guarantees that a team of vehicles reaches consensus on their positions with a zero final velocity while the second algorithm guarantees that a team of vehicles reaches consensus on their positions with a constant final velocity. We show conditions on the sampling period and the control gain such that consensus is reached using these two algorithms over, respectively, an undirected interaction topology and a directed interaction topology. In particular, necessary and sufficient conditions are shown in the case of undirected interaction while sufficient conditions are shown in the case of directed interaction. Consensus equilibria for both algorithms are also given.