Delayed and Switched Deployment of Second-Order Agents on a Line Segment: Delays and Switches Do Not Matter

The problem of the equidistant deployment of mobile agents on a line segment is studied. It is assumed that agent dynamics are modeled by linear second-order models. Two types of control protocols are studied: with and without relative velocity measurements. For any positive damping coefficient of agents, we propose a control protocol that ensures the achievement of the control goal and possesses robustness for any communication delays and any switching topology. The designed multiagent system behavior is illustrated by numerical simulation. The proofs of the results are based on the theory of positive systems.