Synchronization of stochastic reaction-diffusion systems via boundary control

Abstract

This paper studies the problem of mean square asymptotical synchronization and H∞ synchro- nization for coupled stochastic reaction–diffusion sys- tems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptot- ical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient condi- tions are obtained for ensuring mean square asymptoti- cal synchronization. When coupled SRDSs are subject to external disturbance, mean square H∞ synchroniza- tion is investigated and corresponding criterion is pre- sented under a designed boundary controller. In addi- tion to focusing on systems with Neumann bound- ary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient condi- tions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.