Asynchronous containment control for discrete-time second-order multi-agent systems with time-varying delays

The asynchronous containment control problem of second-order discrete-time multi-agent systems with time-varying delays is investigated. Asynchrony in this paper means that each agent updates state information via its clock that is independent of those of the other agents', and the time sequence over which each agent updates its state information is not necessarily equispaced. An asynchronous distributed control protocol is designed to realize local control strategies for the second-order discrete-time multi-agent system. By utilizing the proposed protocol and properties of Laplacian matrix, the asynchronous containment control problem of second-order multi-agent systems is equivalently transformed into a stability problem of synchronous error system. Based on the nonnegative matrix theory and graph theory, a necessary and sufficient condition is obtained to make all the followers asymptotically converge to the convex hull formed by the stationary leaders. Finally, some simulation examples are presented for illustration.