Containment control of second-order multi-agent systems via asynchronous sampled-data control

This paper formulates and solves an asynchronous sampled-data containment control problem of second-order multi-agent systems, in which each agent only receives the neighbors' information at certain sampling instants determined by its own clock, not all sampling instants. It is not assumed that the time sequence in which each agent receives its neighbors' information is evenly spaced. A distributed containment control protocol in the asynchronous sampled-data setting is designed. Main research tools, including nonnegative matrix theory and the composite of binary relation, are used to derive a necessary and sufficient condition guaranteeing that all the followers asymptotically converge to a convex hull formed by the static leaders. An example is provided to demonstrate the effectiveness of our theoretical result.