Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations

Abstract : The feedback stabilization of the Burgers system to a nonstationary solution using finite-dimensional internal controls is considered. Estimates for the dimension of the controller are derived. In the particular case of no constraint on the support of the controla better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed; some numerical examplesare presented illustrating the stabilizing effect of the feedback control, and suggesting that the existence of an estimatein the general case analogous to that in the particular one is plausible.
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Axel Kröner, Sergio S. Rodrigues. Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (2), pp.1020-1055. ⟨hal-01089893⟩

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