Synchronization via impulsive deadbeat coupling

TL;DR

This paper presents a simple impulsive deadbeat coupling method for synchronizing linear networks, achieving exact synchronization after a finite number of periods with sufficiently strong coupling.

Contribution

It introduces a deadbeat feedback control law for impulsive coupling in linear networks, ensuring synchronization in finite time as coupling strength increases.

Findings

Synchronization occurs after n periods at high coupling strength.

Exact synchronization is achieved in the limit as coupling strength approaches infinity.

The method is simple and effective for linear network synchronization.

Abstract

For linear networks, where the coupling between the agents takes place through periodic impulses, a simple method is proposed for synchronization. It is shown that closing the loop by (normalized) deadbeat feedback gain produces synchronous behavior if the coupling strength $\mu$ is large enough. With such choice of control law, in the limiting case ($\mu\to\infty$) exact synchronization is achieved after $n$ periods, where $n$ is the order of individual agent dynamics.