@article{Wang2026, 
author = {Qian Wang and Zi-Peng Wang and Zhiyi Lu and Xiao-Wei Zhang},
title = {H          ∞       boundary control design of spatial 2-D linear stochastic parabolic PDE systems},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {12606-12620},
keywords = {2-D linear stochastic parabolic PDE systems, H∞ boundary control, static output feedback, mean square exponential stability},
url = {https://www.sciopen.com/article/10.3934/math.2026518},
doi = {10.3934/math.2026518},
abstract = {In practical applications involving spatiotemporal processes, the two-dimensional (2-D) spatial scenario is often more relevant. However, higher spatial dimensionality poses a major challenge for control design, drastically increasing its complexity. This work investigated the        H          ∞       boundary control problem for a class of 2-D linear stochastic parabolic partial differential equation (PDE) systems subject to multiplicative noise in the state. We used multidimensional Green's formula and alternative inequalities to handle complex terms in 2-D systems. A static output feedback (SOF) control strategy was introduced to achieve stabilization within a stochastic paradigm. By employing Lyapunov-based technique, a constructive method for SOF controller design was established, ensuring that the closed-loop system achieved exponential stability in the mean square sense with        H          ∞       performance. Numerical simulations of a stochastic thermal process demonstrated the effectiveness and applicability of the proposed control methodology.}
}