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

Backstepping Stabilization of the Linearized Saint-Venant-Exner Model