This paper considers the multi-leader situation in multi-agent systems (MASs), providing a solution to the issue of containment control in MASs using a directed graph as the main focus of the investigation. Containment controllers are first designed for MASs respectively by using boundary measurement and distributed measurement, as well as considering time-invariant and time-varying delays. By making use of the Wirtinger inequality and the Lyapunov Krasovskii function, consensus criteria for containment consensus of the MASs are established. Finally, two numerical examples are given to verify the effectiveness of the proposed protocols.

Boundary containment control of multi-agent systems with time-invariant and time-varying delays