Spatial sampled-data control for stochastic reaction-diffusion systems

This paper considers the control problems for stochastic reaction-diffusion systems (SRDSs) with a spatial sampled-data (SSD) controller. The SSD controller engenders spatial discrete term such that the SRDS with SSD controller is a hybrid system. The coexistence of stochastic disturbance, spatial diffusion and discrete term brings out new challenges for the analysis of system properties. Utilizing the Lyapunov functional and inequality techniques, we establish several criteria on mean square exponential stabilization and robust mean square finite-time stabilization of SRDSs. Moreover, we consider the H_∞ control problem when there exist external disturbances. Both system disturbances and boundary disturbances are included in our model. Sufficient conditions are obtained to ensure the mean square H_∞ performance. The effects of the length of sampled-data interval and the diffusion term on the stability are reflected in all obtained criteria. Numerical simulations verify our theoretical results.