Output-Feedback Synchronizability of Linear Time-Invariant Systems

TL;DR

This paper investigates the output-feedback synchronization of identical linear time-invariant systems, providing a criterion for synchronization, characterizing the class of synchronizable systems, and exploring conditions especially for SISO systems.

Contribution

It introduces a new criterion for network synchronization and characterizes output-feedback synchronizable systems with necessary and sufficient conditions.

Findings

Output-feedback stabilizability is sufficient but not necessary for synchronization.

Conditions for SISO systems are derived in the frequency domain.

The theory is supported by several illustrative examples.

Abstract

The paper studies the output-feedback synchronization problem for a network of identical, linear time-invariant systems. A criterion to test network synchronization is derived and the class of output-feedback synchronizable systems is introduced and characterized by sufficient and necessary conditions. In particular it is observed that output-feedback stabilizability is sufficient but not necessary for output-feedback synchronizability. In the special case of single-input single-output systems, conditions are derived in the frequency domain. The theory is illustrated with several examples.