Artículo
Local Exponential $H^2$ Stabilization of a $2\times2$ Quasilinear Hyperbolic System Using Backstepping
Autor/es | Coron, Jean Michel
Vázquez Valenzuela, Rafael Krstic, Miroslav Bastin, Georges |
Departamento | Universidad de Sevilla. Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos |
Fecha de publicación | 2013 |
Fecha de depósito | 2017-04-19 |
Publicado en |
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Resumen | In this work, we consider the problem of boundary stabilization for a quasilinear
2 × 2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with
actuation on only one end of the domain, ... In this work, we consider the problem of boundary stabilization for a quasilinear 2 × 2 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 H2 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 4 × 4 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. |
Cita | Coron, J.M., Vázquez Valenzuela, R., Krstic, M. y Bastin, G. (2013). Local Exponential ^2$ Stabilization of a \times2$ Quasilinear Hyperbolic System Using Backstepping. SIAM Journal on Control and Optimization, 51 (3), 2005-2035. |