Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays

This paper considers the containment control problem for leader-following multi-agent systems in the presence of dynamically switching topologies with communication delays. Two types of control algorithms are proposed for containment control with first-order dynamics and second-order dynamics. By applying modern control theory and algebraic graph theory, the stabilities of two containment control algorithms are analyzed on Lyapunov-Krasovskii method. Moreover, some sufficient conditions are provided through further researching the connected portion of multi-agent systems, which can ensure that the containment control can be achieved asymptotically when communication topologies are jointly-connected. Finally, some simulation examples are provided to demonstrate the effectiveness of two proposed algorithms.