Boundary stabilization of random reaction-diffusion systems

The boundary stabilization of a class of reaction-diffusion systems perturbed by second-order processes is investigated in this work. It extends the results from random ordinary differential equations to random reaction-diffusion systems (RRDSs). First, the stability analysis of RRDSs with boundary function is presented. Using the Lyapunov method and stochastic process estimation, two criteria of asymptotic stability are established in 2-nd moment and in probability, by applying Wirtinger's inequality and the weak law of large numbers. Second, based on the obtained stability criteria, a class of boundary control problems is solved by constructing a Lyapunov functional and designing integral boundary controllers. Additionally, the influence of nonlinear terms and the diffusion coefficient on stability is analyzed. Finally, numerical simulations demonstrate the effectiveness of the boundary controller.