Delayed and Switched Control of Formations on a Line Segment: Delays and Switches Do Not Matter

The agents' deployment over a line segment under protocols with communication delays and switching is studied. It is assumed that no information about the value of the communication delay and no information about switching policy in the communication graph is available. It is shown that neither delay values nor switching policy in a natural class may influence convergence of the agent states to the equidistant distribution over the line segment. Similar result is obtained for deployment over the circle. The theoretical results are illustrated by simulations. The proofs relay on both well-known and recent approaches to the stability analysis of positive systems.