A Problem of Nonuniform Deployment for a Discrete-time Multiagent System

A discrete-time multiagent system on a line is studied. The case is considered where each agent receives information from some of its neighbors, and there are switching of network topology and communication delays. It is assumed that a segment of the line is given. It is necessary to provide a prescribed nonuniform agent distribution on the segment. A decentralized control protocol is designed. Using the Lyapunov direct method, it is proved that, under this protocol, agents converge to the desired positions for any constant delay and any admissible switching of the network topology.