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Conference Papers Year : 2019

Stabilization of the linear Kuramoto-Sivashinsky equation with a delayed boundary control

Abstract

In this paper we stabilize the linear Kuramoto-Sivashinsky equation by means of a delayed boundary control. From the spectral decomposition of the spatial operator associated to the equation, we find that there is a finite number of unstable eigenvalues. After applying the Artstein transform to deal with the delay phenomenon, we design a feedback law based on the pole-shifting theorem to exponential stabilize the finite-dimensional system associated to the unstable eigenvalues. Then, thanks to the inversion of the Artstein transform and the use of a Lyapunov function, we obtain a delayed feedback law that exponential stabilize the original unstable infinite-dimensional system.
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Dates and versions

hal-02002453 , version 1 (31-01-2019)

Identifiers

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Patricio Guzmán, Swann Marx, Eduardo Cerpa. Stabilization of the linear Kuramoto-Sivashinsky equation with a delayed boundary control. 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019, May 2019, Oaxaca, Mexico. ⟨10.1016/j.ifacol.2019.08.013⟩. ⟨hal-02002453⟩
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