strict Lyapunov function for boundary control with integral actions of
hyperbolic systems of conservation laws that can be diagonalised with
Riemann invariants, is presented. The time derivative of this Lyapunov
function can be made strictly negative definite by an appropriate
choice of the boundary conditions and the integral control gains.
Previous stability results are extended 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 measured only at
the boundaries. The control design method is illustrated with a
hydraulic application, namely the level and flow regulation in a reach
of the Sambre river and in the micro-channel of Valence, respectively
through simulations and experimentations.