Boundary Control for Stochastic Reaction-Diffusion System Cascaded With an ODE System

The control problems are investigated for a stochastic reaction–diffusion system (SRDS) cascaded with an ordinary differential system (ODS). We propose a novel hybrid control strategy that combines boundary control for the SRDS with state feedback control for the ODS. The primary objective is to ensure the cascaded system achieves mean-square exponential stability (MSES). Our research offers a flexible framework for stability analysis and control synthesis in cascaded systems, applicable regardless of the ODS’s inherent stability. We further explore the system’s robust stabilization with uncertainties and its H_{\infty } performance to quantify disturbance-rejection capabilities. The key innovations include the development of a unified control framework that accommodates both stable and unstable ODE subsystems, the design of boundary control inputs that ensure MSES even in the presence of parameter uncertainties, and the application of matrix inequality techniques to simplify controller design. The effectiveness of the proposed control strategies is demonstrated by three numerical examples.