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arXiv · 1208.6475

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

Jean-Michel Coron·Rafael Vazquez·Miroslav Krstic·Georges Bastin
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Abstract

In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2 exponential stability of the closedloop system. Our proof uses a backstepping transformation to find new variables for which a strict Lyapunov function can be constructed. The kernels of the transformation are found to verify a Goursat-type 4X4 system of first-order hyperbolic PDEs, whose well-posedness is shown using the method of characteristics and successive approximations. Once the kernels are computed, the stabilizing feedback law can be explicitly constructed from them.

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Jean-Michel Coron, Rafael Vazquez, Miroslav Krstic, Georges Bastin. 2012-08-31. Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping. https://arxiv.org/abs/1208.6475

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