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In this work, we consider the problem of boundary stabilization for aquasilinear 2X2 system of first-order hyperbolic PDEs. We design a newfull-state feedback control law, with actuation on only one end of the domain,which achieves H^2 exponential stability of the closedloop system. Our proofuses a backstepping transformation to find new variables for which a strictLyapunov function can be constructed. The kernels of the transformation arefound to verify a Goursat-type 4X4 system of first-order hyperbolic PDEs, whosewell-posedness is shown using the method of characteristics and successiveapproximations. Once the kernels are computed, the stabilizing feedback law canbe explicitly constructed from them.

Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping