Numerical discretization of boundary control problems for systems of balance laws: Feedback stabilization

We consider the boundary control of discretized problems based on systems of linear conservation laws including source terms. For a discrete Lyapunov function we prove the exponential decay in L2-norm using first-order finite volume methods. We give explicit computations of the decay rates and apply the proposed framework to the numerical boundary feedback stabilization of electric transmission lines given by the telegraphers equation.