Backstepping control of a wave PDE with unstable source terms and dynamic boundary

Abstract : This paper presents the design of an exponentially stabilizing controller for a one-dimensional wave partial differential equation (PDE). The control is acting on a Robin's boundary condition while the opposite boundary satisfies an unstable dynamic. The wave is also subject to unstable in-domain source terms. Closed-loop exponential stabilization is obtained via a full-state backstepping controller. The existence and uniqueness of this backstepping transformation is proven, using the method of successive approximations.
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  • HAL Id : hal-01815802, version 1

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Christophe Roman, Delphine Bresch-Pietri, Eduardo Cerpa, Christophe Prieur, Olivier Sename. Backstepping control of a wave PDE with unstable source terms and dynamic boundary. IEEE Control Systems Letters, IEEE, 2018, 2 (3), pp.459-464. 〈hal-01815802〉

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