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

TL;DR

This paper presents a method for achieving global asymptotic synchronization of identical neutrally-stable linear systems through linear output feedback, applicable to various network topologies, with an algorithm for feedback law computation.

Contribution

It introduces a feedback law for synchronization of neutrally-stable systems and provides an algorithm to compute it based on system parameters.

Findings

Synchronization is achievable under all fixed connected network topologies.

A constructive algorithm for feedback law computation is provided.

Dual results for stabilizable systems are established.

Abstract

Synchronization of coupled continuous-time linear systems is studied in a general setting. For identical neutrally-stable linear systems that are detectable from their outputs, it is shown that a linear output feedback law exists under which the coupled systems globally asymptotically synchronize under all fixed (directed) connected network topologies. An algorithm is provided to compute one such feedback law based on individual system parameters. The dual case, where individual systems are neutrally stable and stabilizable from their inputs, is also considered and parallel results are established.