Boundary feedback control in networks of open channels

This article deals with the regulation of water flow in open-channels modelled by Saint-Venant equations. By means of a Riemann invariants approach, we deduce stabilizing control laws for a single horizontal reach without friction. The stability condition is extended to a general class of hyperbolic systems which can describe canal networks with more general topologies. A control law design based on this condition is illustrated with a simple case study: two reaches in cascade. The proof of the main stability theorem is based on a previous result from Li Ta-tsien concerning the existence and decay of classical solutions of hyperbolic systems.