Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation

In this paper, we study the exponential stabilization of a shock steady state for the inviscid Burgers equation on a bounded interval. Our analysis relies on the construction of an explicit strict control Lyapunov function. We prove that by appropriately choosing the feedback boundary conditions, we can stabilize the state as well as the shock location to the desired steady state in [Formula: see text]-norm, with an arbitrary decay rate.