Coron, Jean-Michel
[Université Pierre et Marie Curie]
Vazquez, Rafael
[Universidad de Sevilla]
Krstic, Miroslav
[University of California San Diego]
Bastin, Georges
[UCL]
In this work, we consider the problem of boundary stabilization for a quasilinear $2 imes2$ 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 closed-loop 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 $4 imes4$ 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.
Bibliographic reference |
Coron, Jean-Michel ; Vazquez, Rafael ; Krstic, Miroslav ; Bastin, Georges. Local exponential H2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping. In: SIAM Journal on Control and Optimization, Vol. 51, no. 3, p. 2005–2035 (2013) |
Permanent URL |
http://hdl.handle.net/2078.1/123864 |