Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping
Optimization and Control
2012-09-03 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1208.6475,
title = {Local exponential H^2 stabilization of a 2X2 quasilinear hyperbolic system using backstepping},
author = {Jean-Michel Coron and Rafael Vazquez and Miroslav Krstic and Georges Bastin},
journal= {arXiv preprint arXiv:1208.6475},
year = {2012}
}