We present a strict Lyapunov function for hyperbolic systems of
conservation laws that can be diagonalised with Riemann invariants. The
time derivative of this Lyapunov function can be made strictly definite
negative by an appropriate choice of the boundary conditions. It
is shown that the derived boundary control allows to guarantee the
local convergence of the state towards a desired set point.
Furthermore, the control can be implemented as a feedback of the state
only measured at the boundaries. The control design method is
illustrated with an hydraulic application, namely the level and flow
regulation in an horizontal open channel. Full paper.