Synchronization in Networks of Identical Linear Systems

TL;DR

This paper develops a dynamic output feedback method to synchronize networks of identical linear systems with possibly directed and time-varying connections, extending classical consensus algorithms.

Contribution

It introduces a novel dynamic output feedback coupling that guarantees synchronization under broader conditions than static diffusive coupling.

Findings

Synchronization achieved with no exponentially unstable modes.

Dynamic feedback outperforms static diffusive coupling.

Conditions for synchronization are both sufficient and nearly necessary.

Abstract

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient but to some extent, also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature.