Backstepping stabilization of the linearized Saint-Venant-Exner Model: Part II- output feedback

We consider a coupled Saint-Venant-Exner (SVE) model introduced in a companion paper. This studied model describes the 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. It consists of two rightward and one leftward convecting transport Partial Differential Equations (PDEs). A single boundary input control (with actuation located only at downstream) strategy is adopted and the backstepping approach developed for the first order linear hyperbolic PDEs is used. A full state feedback exponentially stabilizing controller is designed in the companion paper. In this paper, we first design an exponentially convergent Luenberger observer. Then, based on the full state controller and reconstruction of the distributed state from the observer, we achieve output feedback exponential stabilization of the model.