On containment control for discrete-time switching networks of delayed first-order systems

This paper delves into the domain of dynamic containment control, with specific focus on discrete-time perturbed and delayed systems characterised by first-order dynamics. Central to containment control is the aspiration to guide agents towards desired spatial formations while mitigating the effects of disturbances, ensuring cohesive behaviour. In this respect, we propose a containment protocol that ensures input-to-state stability with respect to the convex hull generated by the leader trajectories while guaranteeing robustness with respect to both fixed and distributed communication delays acting on the state measurements exchanged between the network nodes. Numerical simulations on a team of interconnected drones show the effectiveness of the proposed approach.