Nonlinear feedback stabilization of a two-dimensional Burgers equation
Université de Toulouse, UPS, Institut de Mathématiques, UMR CNRS 5219, 31062 Toulouse Cedex 9, France. Laetitia.Thevenet@math.univ-toulouse.fr; firstname.lastname@example.org; email@example.com
Revised: 5 May 2009
In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.
Mathematics Subject Classification: 93B52 / 93C20 / 93D15
Key words: Dirichlet control / Neumann control / feedback control / stabilization / Burgers equation / Algebraic Riccati equation
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