Boundary Stabilization and H∞ Control for Stochastic Reaction-Diffusion Systems

This paper discusses the problems of stabilization and H-infinity control for stochastic reaction-diffusion systems(SRDSs) via boundary control. The SRDSs with Neumann boundary condition is considered. Making use of the Lyapunov-Krasoviskii functional method and Ito formula, we obtain the sufficient condition guaranteeing the mean square asymptotical stability under the boundary control. When systems are affected by external disturbances, we investigate the H-infinity control. By utilizing a standard completion of squares argument, we derive the sufficient condition which guarantees the H-infinity performance. At last, we provide examples to illustrate the effectiveness of our results.