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arXiv · 2201.00343

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

Abbas Kabalan·Francesco Ferrante·Giacomo Casadei·Andrea Cristofaro·Christophe Prieur
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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.

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Abbas Kabalan, Francesco Ferrante, Giacomo Casadei, Andrea Cristofaro, Christophe Prieur. 2022-01-02. Leader-Follower Synchronization of a Network of Boundary-Controlled Parabolic Equations With In-Domain Coupling. https://doi.org/10.1109/lcsys.2021.3136097

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