Abstract | ||
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In this work, we consider the boundary stabilization of a linear diffusion equation coupled with a linear transport equation. This type of hyperbolic-parabolic partial differential equations (PDEs) coupling arises in many biological, chemical and thermal systems. The two equations are coupled inside the domain and at the boundary. The in-domain coupling architecture is considered from both sides i.e. an advection source term driven by the transport PDE and a Volterra integral source term driven by the parabolic PDE. Using a backstepping method, we derive two feedback control laws and we give sufficient conditions for the exponential stability of the coupled system in the L-2 norm. Controller gains are calculated by solving hyperbolic-parabolic kernel equations arising from the backstepping transformations. The theoretical results are illustrated by numerical simulations. |
Year | DOI | Venue |
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2020 | 10.23919/ACC45564.2020.9147593 | 2020 AMERICAN CONTROL CONFERENCE (ACC) |
DocType | ISSN | Citations |
Conference | 0743-1619 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
---|---|---|---|
Mohammad Ghousein | 1 | 0 | 0.68 |
Emmanuel Witrant | 2 | 76 | 11.27 |