We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in ℝ d . Using a Lyapunov function with a suited weight function depending on the system under consideration we show stabilization in L 2 for the studied system using a suitable feedback control. Therefore the controllability of the studied system is related to the feasibility of an associated linear matrix inequality.We show the applicability discussing the barotropic Euler equations.
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Herty et al. (2024) studied this question.
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