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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2013

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

Résumé

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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Dates et versions

hal-00726867 , version 1 (31-08-2012)

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Jean-Michel Coron, Rafael Vazquez, Miroslav Krstic, Georges Bastin. Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping. SIAM Journal on Control and Optimization, 2013, 51 (3), pp.2005--2035. ⟨10.1137/120875739⟩. ⟨hal-00726867⟩
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