Fredholm Transform and Local Rapid Stabilization for a Kuramoto-Sivashinsky Equation

By Jean-Michel Coron, Qi Lu. 2015

63 citations recorded by the source corpus.

This paper is devoted to the study of the local rapid exponential stabilization problem for a controlled Kuramoto-Sivashinsky equation on a bounded interval. We build a feedback control law to force the solution of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates, provided that the initial datum is small enough. Our approach uses a method we introduced for the rapid stabilization of a Korteweg-de Vries equation. It relies on the construction of a suitable integral transform and can be applied to many other equations.

Subfields: Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e1a150f388f547246086ebcde1090ebd2d60b113

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In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Stabilization and controllability of first-order integro-differential hyperbolic equations (2015, methodology): “Finally, let us point out that Fredholm transformations have also been used to prove the exponential stabilization for a Korteweg-de Vries equation in [9] and for a Kuramoto-Sivashinsky equation in [10].”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, background): “See, in particular, [2] forwave equations, [3] for compensating the distributed effect of diffusion and counter-convection inMulti-Input andMulti-Output LTI systems, [7] for KdV equations, [8] for Kuramoto–Sivashinsky equations.”