Boundary Feedback Stabilization and Control of Star-shaped Open Canals

This paper considers the boundary control of a star-shaped open-channel network modeled by the Saint-Venant equations. We present the boundary feedback stabilization of the Saint-Venant equations by means of a Riemann invariants method. The estimation of the parameters satisfying the stability condition is deduced. The boundary feedback control is developed to guarantee that the solution of the control system decays exponentially, only by taking the water levels at the gate boundaries as the feedback.