STABILIZATION OF A MULTI-DIMENSIONAL SYSTEM OF HYPERBOLIC BALANCE LAWS

. We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in 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.

Automated summary

In this paper, we investigate the feedback stabilization problem for systems described by Hamilton-Jacobi type equations in R-n. By reformulating the problem, a stabilization problem for a multi-dimensional system of n hyperbolic partial differential equations is obtained. Using a novel Lyapunov function that takes into account the multi-dimensional geometry, we prove the stabilization of the resulting system in L(2) through suitable feedback control. We also provide examples based on the forming process to illustrate such systems.