Local exponential H2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping
(2013) SIAM Journal on Control and Optimization — Vol. 51, n° 3, p. 2005-2035 (2013)
Files
paper98.pdf
Restricted Access - Adobe PDF
- 555.07 KB
Details
- Authors
Bastin, Georges 
- Abstract
- 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.
- Affiliations
Citations
Coron, J.-M., Vazquez, R., Krstic, M., & Bastin, G. (2013). Local exponential H2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping. SIAM Journal on Control and Optimization, 51(3), 2005-2035. https://doi.org/10.1137/120875739 (Original work published 2013)