Consensus of Double Integrator Multiagent Systems under Nonuniform Sampling and Changing Topology

TL;DR

This paper addresses the consensus problem in multiagent systems with double integrator dynamics under nonuniform sampling and changing topologies, providing explicit controller bounds and a novel contraction-based condition.

Contribution

It introduces a new sufficient condition for consensus using contraction theory, applicable to systems with nonuniform sampling and dynamic, balanced topologies.

Findings

Consensus can be achieved with arbitrary maximum sampling time.

Explicit bounds for controller parameters are derived.

The contraction-based condition generalizes to dynamic topologies.

Abstract

This article considers consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. It is considered the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in a given region, which can be selected arbitrarily. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are balanced and has a spanning tree. Also, explicit bounds for controller parameters are given. A novel sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of balanced topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.