L 2 – L ∞ containment control of multi‐agent systems with Markovian switching topologies and non‐uniform time‐varying delays

Abstract

In this study, the authors investigate L 2 − L ∞ 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 ∞ 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 ∞ performance. Two numerical simulations are provided to show the effectiveness of theoretical results.