Stabilization of a multi-dimensional system of hyperbolic balance laws

Abstract

We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $ \mathbb{R}^n $. A reformulation leads to a stabilization problem for a multi-dimensional system of $ n $ hyperbolic partial differential equations. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in $ L^2 $ for the arising system using a suitable feedback control. We further present examples of such systems partially based on a forming process.