BOUNDARY CONTROL OF SYSTEMS OF CONSERVATION LAWS : LYAPUNOV STABILITY WITH INTEGRAL ACTIONS

A boundary control law with integral actions is proposed for a generic class of two-by-two homogeneous systems of linear conservation laws. Sufficient conditions on the tuning parameters are stated that guarantee the asymptotic stability of the closed-loop system. The closed-loop stability is analysed with an appropriate Lyapunov function. The control design method is validated with an experimental application to the regulation of water depth and flow rate in a pilot open-channel described by Saint-Venant equations. This hydraulic application shows that the control can be robustly implemented on nonhomogeneous systems of nonlinear conservation laws.