Local explicit feedback boundary conditions are given for the stabilization in L2−norm of the 2-D shallow
water model. The proposed method is based on symmetrization of the flux matrices of the linearized model and analysis of the Riemann invariants. The non-conservative 2-D shallow water equations are linearized around the target steady state sub-critical flow. The established feedback control laws guarantee a decay of the energy of the perturbation model.
We present numerical simulations to demonstrate how the proposed controller works for the linearized as well as nonlinear shallow water problem.