Containment control for asynchronous sampled-data second-order multi-agent systems under switching topologies

A containment control problem is discussed in this paper for asynchronous sampled-data second-order multi-agent systems under switching topologies, where the sampled time instants that each follower receives the state information of its neighbors is independent of other agents. First, the asynchronous containment control problem is transformed into a convergence problem of the product of infinite time-varying nonnegative matrices. Then by exploring the relationship between the product of matrices and the composition of the corresponding graphs, we obtain a sufficient condition in terms of the communication topologies to ensure the containment control. Finally, a simulation example is illustrated for the effectiveness of the theoretical result.