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In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and <italic>in-domain</italic> 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.

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