Leader-Follower Synchronization of a Network of Boundary-Controlled Parabolic Equations With In-Domain Coupling

TL;DR

This paper investigates leader-follower synchronization in networks of boundary-controlled parabolic PDEs with in-domain coupling, providing conditions for exponential synchronization and supporting results with numerical simulations.

Contribution

It introduces a novel framework for analyzing leader-follower synchronization in PDE networks with boundary control and in-domain coupling, including matrix inequality conditions for control parameter selection.

Findings

Derived sufficient matrix inequality conditions for exponential synchronization.

Validated theoretical results through numerical simulations.

Extended synchronization analysis to in-domain coupled parabolic PDE networks.

Abstract

In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and in-domain coupling. We describe the problem in an abstract formulation and we specialize it to a network of parabolic partial differential equations. We consider a setting in which a subset of the followers is connected to the leader through a boundary control, while interconnections among the followers are enforced by distributed in-domain couplings. Sufficient conditions in the form of matrix inequalities for the selection of the control parameters enforcing exponential synchronization are given. Numerical simulations illustrate and corroborate the theoretical findings.