Discrete-Time Distributed Observers over Jointly Connected Switching Networks and an Application

TL;DR

This paper develops discrete-time distributed observers for switching networks, proving stability, and applying them to leader-following, consensus, and formation control problems in multi-agent systems.

Contribution

It introduces adaptive distributed observers that do not require followers to know the leader's system matrix, extending existing methods.

Findings

Established exponential stability for linear switched systems.

Designed adaptive distributed observers for leader systems.

Applied to cooperative output regulation and formation control.

Abstract

In this paper, we first establish an exponential stability result for a class of linear switched systems and then apply this result to show the existence of the distributed observer for a discrete-time leader system over jointly connected switching networks. A special case of this result leads to the solution of a leader-following consensus problem of multiple discrete-time double-integrator systems over jointly connected switching networks. Then, we further develop the adaptive distributed observer for the discrete-time leader system over jointly connected switching networks, which has the advantage over the distributed observer in that it does not require that every follower know the system matrix of the leader system. As an application of the discrete-time distributed observer, we will solve the cooperative output regulation problem of a discrete-time linear multi-agent system over jointly connected switching networks. A leader-following formation problem of mobile robots will be used to illustrate our design. This problem cannot be handled by any existing approach.