Geometry of deadbeat synchronization

TL;DR

This paper investigates the geometric properties of deadbeat synchronization in discrete-time nonlinear systems, demonstrating finite-step synchronization through compatible observer and interconnection design, with an illustrative example.

Contribution

It introduces a geometric framework for deadbeat synchronization and establishes conditions for finite-time convergence in coupled nonlinear systems.

Findings

Synchronization achieved in finite steps under compatibility conditions

Geometric approach clarifies the structure of deadbeat synchronization

Example with third-order observers illustrates the theory

Abstract

The deadbeat synchronization of identical discrete-time nonlinear systems is studied from a geometric point of view. An array of deadbeat observers coupled via a deadbeat interconnection is shown to achieve synchronization in finite number of steps provided that a compatibility condition is satisfied between the observer and the interconnection. As an illustration to the theory, an example is provided where an array of third order observers achieves deadbeat synchronization.