Finite-time boundary stabilization for Korteweg–de Vries–Burgers equations

Abstract

The finite-time boundary stabilization is investigated for Korteweg–de Vries–Burgers (KdVB) equations. Firstly, a distributed controller is derived, and criteria are presented to guarantee the finite-time stability (FTS) of KdVB equations via the distributed controller. Then, considering the installation in real applications, a vogue control strategy, a boundary controller design, is adopted to ensure the FTS. In light of the FTS lemma, sufficient conditions are obtained for KdVB equations to ensure the FTS. When there exist uncertainties in the system’s coefficients, the robust finite-time stabilization is studied for uncertain KdVB equations. With the designed boundary controller, a sufficient condition is provided to ensure the FTS for the uncertain KdVB equation. Finally, the theoretical results are verified by numerical examples.