Synchronizing discrete-time neutrally stable linear systems via partial-state coupling

TL;DR

This paper demonstrates that for neutrally stable, detectable discrete-time linear systems, a linear output feedback law can be designed to ensure global asymptotic synchronization across various network topologies.

Contribution

It provides a method to compute a feedback law for synchronization in neutrally stable systems, extending the understanding of output coupling in linear system networks.

Findings

Existence of a linear feedback law for synchronization.

Algorithm for computing the feedback law.

Synchronization achieved for all connected network topologies.

Abstract

A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law exists under which the coupled systems globally asymptotically synchronize for all fixed connected (asymmetrical) network topologies. An algorithm is provided to compute such feedback law based on individual system parameters. A dual problem is also presented and solved.