Discrete-time Deployment of Agents on a Line Segment: Delays and Switches Do Not Matter

Abstract

This paper considers the discrete-time problem of deploying agents on a line segment under delay in communication channels and switching and also under incomplete information about the value of the delay and the law of switching. It is shown that neither delay nor switching affect the convergence of the agents' states to the uniform allocation on the line segment. The theoretical results are illustrated by numerical simulation. The evidence is based on the well-known and new approaches to the stability analysis of positive systems.