LQR-based coupling gain for synchronization of linear systems

TL;DR

This paper presents a method for synchronizing coupled linear systems using LQR-based feedback, with conditions on coupling strength derived from eigenvalue analysis, applicable to both stabilizable and detectable systems.

Contribution

It introduces an LQR-based feedback approach for synchronization in coupled linear systems, extending to output-coupled systems and providing eigenvalue-based coupling strength criteria.

Findings

Synchronization achieved with strong enough coupling.

Applicable to both stabilizable and detectable systems.

Provides explicit eigenvalue-based coupling conditions.

Abstract

Synchronization control of coupled continuous-time linear systems is studied. For identical systems that are stabilizable, a linear feedback law obtained via algebraic Riccati equation is shown to synchronize any fixed directed network of any number of coupled systems provided that the coupling is strong enough. The strength of coupling is determined by the smallest distance of a nonzero eigenvalue of the coupling matrix to the imaginary axis. A dual problem where detectable systems that are coupled via their outputs is also considered and solved.