L2-L∞ containment control of multi-agent systems with Markovian switching topologies and non-uniform time-varying delays

In this study, the authors investigate L-2 - L-infinity containment control problem of multi-agent systems with multiple stationary leaders and external disturbances. Furthermore, the interaction topology is Markovian switching and non-uniform time-varying delays are considered. By using a model transformation, the containment control problem of the multi-agent systems is turned into a normal L-2 - L-infinity control problem. Based on the theory in stochastic stability for time-delays systems, sufficient conditions in terms of a set of linear matrix inequalities are given to ensure that all the followers will move into the convex hull formed by the leaders in mean square sense with a prescribed L-2 - L-infinity performance. Two numerical simulations are provided to show the effectiveness of theoretical results.