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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2019

Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control

Emmanuel Trélat

Résumé

The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed. To do that we decompose the infinite-dimensional system into two parts: one finite-dimensional unstable part, and one stable infinite-dimensional part. An finite-dimensional delay controller is computed for the unstable part, and it is shown that this controller succeeds in stabilizing the whole partial differential equation. The proof is based on a an explicit form of the classical Artstein transformation, and an appropriate Lyapunov function. A numerical simulation illustrate the constructive design method.
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Dates et versions

hal-01583199 , version 1 (07-09-2017)
hal-01583199 , version 2 (18-04-2019)

Identifiants

Citer

Christophe Prieur, Emmanuel Trélat. Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control. IEEE Transactions on Automatic Control, 2019, 64 (4), pp.1415-1425. ⟨10.1109/TAC.2018.2849560⟩. ⟨hal-01583199v2⟩
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