Distributed containment control for asynchronous discrete-time second-order multi-agent systems with switching topologies

A distributed containment control problem for asynchronous discrete-time second-order multi-agent systems with switching topologies is studied in this paper, where asynchrony means that each agent only receives the state information of its neighbors at certain discrete time instants determined by its own clock that is independent of other agents. Based on a novel containment control protocol, the asynchronous system is transformed into a matrix-vector form, which implies that the asynchronous containment control problem can be converted to a convergence problem of the product of infinite time-varying nonnegative matrices whose all row sums are less than or equal to 1. Then the relations between switching communication topologies and the composite of binary relation are exploited to solve this convergence problem. Finally, we obtain a sufficient condition that all the followers can enter and keep moving in the convex hull formed by the leaders if the union of the effective communication topologies across any time intervals with some given length contains a spanning forest rooted at the leaders. Moreover, some simulation examples are presented for illustration.