Abstract
We consider the problem of boundary stabilization for a quasilinear 2×2 system of first-order hyperbolic PDEs. We design a full-state feedback control law, with actuation on only one end of the domain, and prove local H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> exponential stability of the closed-loop system. The proof of stability is based on the construction of a strict Lyapunov function. The feedback law is found using the recently developed backstepping method for 2 × 2 system of first-order hyperbolic linear PDEs, developed by the authors in a previous work, which is briefly reviewed.
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