Containment Control for Multi-Agent Systems under Directed Interaction Topologies with Time-Varying Delays

This paper is concerned with the containment control problem for multi-agent systems(MASs) with time-varying delays. For the purpose of obtaining less conservative containment control criterion, an augmented Lyapunov-Krasovskii functional(LKF) considering more delay information is constructed firstly. Then by employing the Wirtinger-based integral inequality(WBII) and the extended reciprocally convex matrix inequality(ERCMI) to estimate the derivative of LKF, the delay-dependent term ignored in previous works is reconsidered. Moreover, a delay-product-type(DPT) functional based on the Jensen inequality is established to further reduce the conservatism of the outcomes. As a result, two new criteria are derived to ensure the containment consensus on the communication directed graph, the upper bound of maximum delays and feedback gains. Finally, two numerical simulations are employed to demonstrate the superiority of the theoretical results.