Synchronization under matrix-weighted Laplacian

TL;DR

This paper investigates synchronization of linear systems with pairwise couplings defined by matrix weights, proposing methods to design coupling gains that guarantee convergence in both continuous and discrete time.

Contribution

It introduces simple techniques to generate linear coupling gains for each system pair, ensuring synchronization under matrix-weighted Laplacian conditions.

Findings

Synchronization achieved with the proposed gains

Applicable to both continuous-time and discrete-time systems

Ensures convergence to a common trajectory

Abstract

Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain for each pair of systems, which ensures that all the solutions converge to a common trajectory. Both continuous-time and discrete-time cases are considered.