Robust Finite-Time Stabilization of Stochastic Parabolic PDE Systems via Non-Fragile Spatial Sampled-Data Control

This paper addresses the robust finite-time stabi-lization (FTS) issue for stochastic parabolic PDE systems via non-fragile spatial sampled-data control scheme. First, a class of distributed parameter systems characterized by the delayed stochastic parabolic partial differential equation is developed for analyzing the effects of stochastic disturbance, structural uncertainty, and discrete delay on the system performance. Then, a non-fragile spatial sampled-data control scheme is established by setting sampling points in the spatial domain, which effectively saves communication resources and ensures that the closed-loop system maintains good performance when the controller is perturbed. Moreover, based on the partial differential equation theory, stochastic analysis approach, and the extended Wirtinger's inequality technique, several criteria are provided to ensure the robust FTS of stochastic parabolic PDE systems in the mean square sense. Lastly, a numerical example is provided to verify the feasibility of the suggested stabilization criteria and control scheme.