Boundary control of non-homogeneous systems of two conservation laws

We investigate the problem of the stability of a system of two conservation laws perturbed by non-homogeneous terms. We assume that these non-homogeneous terms have a small C¹-norm. By a Riemann coordinates approach we state a sufficient criterion for the stability in terms of the boundary conditions. This stability result is then applied to the problem of the regulation of the water level and the flow rate in an open channel. The flow in the channel is represented by the SaintVenant equations perturbed by small non-homogeneous terms that account for the friction effects as well as external water supplies or withdrawals.