Exponential Stabilization of Reaction–Diffusion Systems Via Intermittent Boundary Control

Abstract

Exponential stabilization is studied for reaction–diffusion systems (RDSs) with a reaction term satisfying the global Lipschitz condition by means of intermittent boundary control.First, a state-dependent intermittent boundary controller is designed when system states are available. By employing the spatial integral functional method and Poincaré’s inequality, a sufficient condition ensuring exponential stability of RDSs is presented. Then, an observer is presented to estimate the system states based on boundary output, when the information of system states is not fully accessible. An observer-based intermittent boundary controller is provided aiming to stabilize the considered RDSs based on the designed observer. Furthermore, a robust observer-based intermittent boundary controller is proposed to ensure the exponential stability for RDSs with uncertainties. Examples are given to illustrate the effectiveness of results.