Containment control of double-integrator multi-agent systems with aperiodic sampling: A small-gain theorem based method

In this paper, the containment control problem of continuous-time double-integrator multi-agent systems is investigated. An aperiodic sampled-data based protocol is induced by using neighboring information with uncertainly time-varying sampling intervals. With the obtained protocol and properties of Laplacian matrix, the containment control problem of continuous-time multi-agent systems is equivalently transformed into a stability problem of discrete-time systems. By fixing a sampling length in the given range, a time-invariant discrete-time system is obtained. Then the systems with variation of sampling intervals can be considered as uncertain systems of the time-invariant discrete-time system. By using small-gain theorem, sufficient conditions are obtained to guarantee stability of uncertain discrete-time systems. The theoretical results are illustrated by some simulations.