  Using the backstepping design, we achieve exponential stabilization of the
coupled Saint-Venant-Exner (SVE) PDE model of water dynamics in a
sediment-filled canal with arbitrary values of canal bottom slope, friction,
porosity, and water-sediment interaction under subcritical or supercritical
flow regime. The studied SVE model consists of two rightward convecting
transport Partial Differential Equations (PDEs) and one leftward convecting
transport PDE. A single boundary input control (with actuation located only at
downstream) strategy is adopted. A full state feedback controller is firstly
designed, which guarantees the exponential stability of the closed-loop control
system. Then, an output feedback controller is designed based on the
reconstruction of the distributed state with a backstepping observer. It also
guarantees the exponential stability of the closed-loop control system. The
flow regime depends on the dimensionless Froude number Fr, and both our
controllers can deal with the subcritical (Fr < 1) and supercritical (Fr > 1)
flow regime. They achieve the exponential stability results without any
restrictive conditions in contrast to existing results.
