Finite-time boundary stabilization of reaction-diffusion systems

Abstract

In this paper, the problem of boundary finite-time stabilization is considered for reaction-diffusion systems (RDSs). First, a full-domain controller is designed and sufficient conditions are given to ensure finite-time stability of RDSs under the designed controller. Then, for practical applications, a boundary controller is designed to obtain finite-time stability. By virtue of the finite-time stability lemma, criteria are presented to guarantee the finite-time stability of RDSs for the Neumann boundary conditions and mixed boundary conditions. As an extension to uncertain RDSs, robust finite-time stabilization is studied and criterion is obtained under the boundary control. Numerical simulations verify the effectiveness of the proposed design techniques.