Boundary control of stochastic reaction-diffusion systems with Markovian switching

This article focuses on the boundary control of stochastic Markovian reaction-diffusion systems (SMRDSs). Both the cases of completely known and partially unknown transition probabilities are taken into account. By using the Lyapunov functional method, a sufficient condition is obtained under the designed boundary controllers to guarantee the asymptotic mean square stability for SMRDSs with completely known transition probabilities. For the case of partially unknown transition probabilities, we introduce free-connection weighting matrices to handle the boundary control problem. When external disturbance enters the system, a sufficient criterion of H-infinity boundary control is developed. Furthermore, robust stabilization is investigated for parametric uncertain SMRDSs in both cases. Two examples are presented to demonstrate the efficiency of the proposed approaches.