  We study the exponential stability in the $H^{2}$ norm of the nonlinear
Saint-Venant (or shallow water) equations with arbitrary friction and slope
using a single Proportional-Integral (PI) control at one end of the channel.
Using a good but simple Lyapunov function we find a simple and explicit
condition on the gain the PI control to ensure the exponential stability of any
steady-states. This condition is independent of the slope, the friction
coefficient, the length of the river, the inflow disturbance and, more
surprisingly, can be made independent of the steady-state considered. When the
inflow disturbance is time-dependent and no steady-state exist, we still have
the Input-to-State stability of the system, and we show that changing slightly
the PI control enables to recover the exponential stability of slowly varying
trajectories.
