Distributed containment control for first-order and second-order multiagent systems with arbitrarily bounded delays

This paper studies containment control with communication delays and switching topologies. Firstly, a containment control algorithm for first-order discrete-time followers is proposed. Then, it is extended to handle double-integrator dynamics. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to verify the nonincreasing monotonicity of the largest distance from the followers to the convex hull. It is shown that both algorithms are robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to illustrate the effectiveness of the theoretical results.