Rapid and finite-time stabilization of hyperbolic systems with a distributed scalar input

Abstract

We discuss recently obtained stabilization results of hyperbolic systems in one space dimension, with a scalar internal control. These results are obtained using a form of backstepping method, where the systems are mapped to stable target systems using general kernel operators. This method yields explicit feedbacks that achieve exponential stabilization. In some cases, finite-time stabilization can be achieved, with a positive minimal time.