Stability of Boundary Feedback Control Based on Weighted Lyapunov Function in Networks of Open Channels

A Lyapunov function is constructed based on the weighted sum of entropies for the case of two open channels in cascade, which is described by the Saint-Venant equations. A class of boundary feedback controllers is presented to guarantee the local closed-loop asymptotic stability in a neighborhood of the equilibrium point by means of the Lyapunov design approach.